LMFDB - Embedded newform 630.2.i.h.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("630.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} + 14 x^{10} - 28 x^{9} + 36 x^{8} - 24 x^{7} + 33 x^{6} + 42 x^{5} + 114 x^{4} + \cdots + 79 $ x^12 - 5x^11 + 14x^10 - 28x^9 + 36x^8 - 24x^7 + 33x^6 + 42x^5 + 114x^4 + 104x^3 + 197x^2 + 166*x + 79
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.4
Root			$0.429413 + 1.63537i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.h.121.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.400725 + 1.68506i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.400725 + 1.68506i) q^{6} +(0.0665372 - 2.64491i) q^{7} +1.00000 q^{8} +(-2.67884 + 1.35049i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.400725 + 1.68506i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.400725 + 1.68506i) q^{6} +(0.0665372 - 2.64491i) q^{7} +1.00000 q^{8} +(-2.67884 + 1.35049i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.14565 + 3.71637i) q^{11} +(0.400725 + 1.68506i) q^{12} +(2.19516 + 3.80213i) q^{13} +(0.0665372 - 2.64491i) q^{14} +(1.65967 + 0.495491i) q^{15} +1.00000 q^{16} +(2.45730 - 4.25616i) q^{17} +(-2.67884 + 1.35049i) q^{18} +(1.97536 + 3.42143i) q^{19} +(0.500000 - 0.866025i) q^{20} +(4.48350 - 0.947763i) q^{21} +(2.14565 + 3.71637i) q^{22} +(-0.888355 + 1.53868i) q^{23} +(0.400725 + 1.68506i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.19516 + 3.80213i) q^{26} +(-3.34913 - 3.97283i) q^{27} +(0.0665372 - 2.64491i) q^{28} +(2.79745 - 4.84532i) q^{29} +(1.65967 + 0.495491i) q^{30} -3.53789 q^{31} +1.00000 q^{32} +(-5.40249 + 5.10479i) q^{33} +(2.45730 - 4.25616i) q^{34} +(-2.25729 - 1.38008i) q^{35} +(-2.67884 + 1.35049i) q^{36} +(2.40909 + 4.17267i) q^{37} +(1.97536 + 3.42143i) q^{38} +(-5.52715 + 5.22257i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-2.29064 - 3.96751i) q^{41} +(4.48350 - 0.947763i) q^{42} +(4.90148 - 8.48962i) q^{43} +(2.14565 + 3.71637i) q^{44} +(-0.169863 + 2.99519i) q^{45} +(-0.888355 + 1.53868i) q^{46} -12.2426 q^{47} +(0.400725 + 1.68506i) q^{48} +(-6.99115 - 0.351971i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(8.15658 + 2.43514i) q^{51} +(2.19516 + 3.80213i) q^{52} +(-4.18972 + 7.25681i) q^{53} +(-3.34913 - 3.97283i) q^{54} +4.29130 q^{55} +(0.0665372 - 2.64491i) q^{56} +(-4.97373 + 4.69965i) q^{57} +(2.79745 - 4.84532i) q^{58} -11.0744 q^{59} +(1.65967 + 0.495491i) q^{60} -5.47846 q^{61} -3.53789 q^{62} +(3.39368 + 7.17516i) q^{63} +1.00000 q^{64} +4.39032 q^{65} +(-5.40249 + 5.10479i) q^{66} +9.14081 q^{67} +(2.45730 - 4.25616i) q^{68} +(-2.94875 - 0.880345i) q^{69} +(-2.25729 - 1.38008i) q^{70} -4.03887 q^{71} +(-2.67884 + 1.35049i) q^{72} +(4.69222 - 8.12716i) q^{73} +(2.40909 + 4.17267i) q^{74} +(1.25894 - 1.18957i) q^{75} +(1.97536 + 3.42143i) q^{76} +(9.97226 - 5.42778i) q^{77} +(-5.52715 + 5.22257i) q^{78} -1.10226 q^{79} +(0.500000 - 0.866025i) q^{80} +(5.35236 - 7.23548i) q^{81} +(-2.29064 - 3.96751i) q^{82} +(3.33570 - 5.77760i) q^{83} +(4.48350 - 0.947763i) q^{84} +(-2.45730 - 4.25616i) q^{85} +(4.90148 - 8.48962i) q^{86} +(9.28565 + 2.77222i) q^{87} +(2.14565 + 3.71637i) q^{88} +(-6.54765 - 11.3409i) q^{89} +(-0.169863 + 2.99519i) q^{90} +(10.2024 - 5.55302i) q^{91} +(-0.888355 + 1.53868i) q^{92} +(-1.41772 - 5.96154i) q^{93} -12.2426 q^{94} +3.95072 q^{95} +(0.400725 + 1.68506i) q^{96} +(0.883722 - 1.53065i) q^{97} +(-6.99115 - 0.351971i) q^{98} +(-10.7668 - 7.05790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{14} + 7 q^{15} + 12 q^{16} + 7 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} + 17 q^{21} - 7 q^{22} - 9 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} + 7 q^{30} - 18 q^{31} + 12 q^{32} + 3 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} + 14 q^{38} - 14 q^{39} + 6 q^{40} + q^{41} + 17 q^{42} + 7 q^{43} - 7 q^{44} - 5 q^{45} - 9 q^{46} - 14 q^{47} + 2 q^{48} - 24 q^{49} - 6 q^{50} - 3 q^{51} + 2 q^{52} + 2 q^{53} + 11 q^{54} - 14 q^{55} + 8 q^{56} - 14 q^{57} - 9 q^{58} - 58 q^{59} + 7 q^{60} + 22 q^{61} - 18 q^{62} - 13 q^{63} + 12 q^{64} + 4 q^{65} + 3 q^{66} + 44 q^{67} + 7 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - 4 q^{72} + 6 q^{73} - 12 q^{74} + 5 q^{75} + 14 q^{76} - 23 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} - 4 q^{81} + q^{82} - 26 q^{83} + 17 q^{84} - 7 q^{85} + 7 q^{86} - 12 q^{87} - 7 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} - 26 q^{93} - 14 q^{94} + 28 q^{95} + 2 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^14 + 7 * q^15 + 12 * q^16 + 7 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 + 17 * q^21 - 7 * q^22 - 9 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 + 7 * q^30 - 18 * q^31 + 12 * q^32 + 3 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 + 14 * q^38 - 14 * q^39 + 6 * q^40 + q^41 + 17 * q^42 + 7 * q^43 - 7 * q^44 - 5 * q^45 - 9 * q^46 - 14 * q^47 + 2 * q^48 - 24 * q^49 - 6 * q^50 - 3 * q^51 + 2 * q^52 + 2 * q^53 + 11 * q^54 - 14 * q^55 + 8 * q^56 - 14 * q^57 - 9 * q^58 - 58 * q^59 + 7 * q^60 + 22 * q^61 - 18 * q^62 - 13 * q^63 + 12 * q^64 + 4 * q^65 + 3 * q^66 + 44 * q^67 + 7 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - 4 * q^72 + 6 * q^73 - 12 * q^74 + 5 * q^75 + 14 * q^76 - 23 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 - 4 * q^81 + q^82 - 26 * q^83 + 17 * q^84 - 7 * q^85 + 7 * q^86 - 12 * q^87 - 7 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 - 26 * q^93 - 14 * q^94 + 28 * q^95 + 2 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.400725	+	1.68506i	0.231358	+	0.972869i
$3$	0.400725	+	1.68506i	0.231358	+	0.972869i
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.400725	+	1.68506i	0.163595	+	0.687922i
$7$	0.0665372	−	2.64491i	0.0251487	−	0.999684i
$7$	0.0665372	−	2.64491i	0.0251487	−	0.999684i
$8$	1.00000			0.353553
$9$	−2.67884	+	1.35049i	−0.892947	+	0.450163i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.14565	+	3.71637i	0.646938	+	1.12053i	0.983850	+	0.178993i	$0.0572840\pi$
$11$	2.14565	+	3.71637i	0.646938	+	1.12053i	−0.336912	+	0.941536i	$0.609383\pi$
$12$	0.400725	+	1.68506i	0.115679	+	0.486434i
$13$	2.19516	+	3.80213i	0.608827	+	1.05452i	0.991434	+	0.130609i	$0.0416932\pi$
$13$	2.19516	+	3.80213i	0.608827	+	1.05452i	−0.382607	+	0.923911i	$0.624974\pi$
$14$	0.0665372	−	2.64491i	0.0177828	−	0.706883i
$15$	1.65967	+	0.495491i	0.428524	+	0.127935i
$16$	1.00000			0.250000
$17$	2.45730	−	4.25616i	0.595982	−	1.03227i	−0.397425	−	0.917634i	$-0.630096\pi$
$17$	2.45730	−	4.25616i	0.595982	−	1.03227i	0.993407	−	0.114637i	$-0.0365704\pi$
$18$	−2.67884	+	1.35049i	−0.631409	+	0.318313i
$19$	1.97536	+	3.42143i	0.453179	+	0.784929i	0.998581	−	0.0532451i	$-0.0169565\pi$
$19$	1.97536	+	3.42143i	0.453179	+	0.784929i	−0.545402	+	0.838174i	$0.683623\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	4.48350	−	0.947763i	0.978379	−	0.206819i
$22$	2.14565	+	3.71637i	0.457454	+	0.792334i
$23$	−0.888355	+	1.53868i	−0.185235	+	0.320836i	−0.943656	−	0.330929i	$-0.892638\pi$
$23$	−0.888355	+	1.53868i	−0.185235	+	0.320836i	0.758421	+	0.651765i	$0.225971\pi$
$24$	0.400725	+	1.68506i	0.0817976	+	0.343961i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.19516	+	3.80213i	0.430506	+	0.745658i
$27$	−3.34913	−	3.97283i	−0.644540	−	0.764571i
$28$	0.0665372	−	2.64491i	0.0125744	−	0.499842i
$29$	2.79745	−	4.84532i	0.519473	−	0.899754i	−0.480271	−	0.877120i	$-0.659462\pi$
$29$	2.79745	−	4.84532i	0.519473	−	0.899754i	0.999744	−	0.0226333i	$-0.00720503\pi$
$30$	1.65967	+	0.495491i	0.303012	+	0.0904639i
$31$	−3.53789			−0.635423			−0.317712	−	0.948187i	$-0.602914\pi$
$31$	−3.53789			−0.635423			−0.317712	+	0.948187i	$0.602914\pi$
$32$	1.00000			0.176777
$33$	−5.40249	+	5.10479i	−0.940453	+	0.888629i
$34$	2.45730	−	4.25616i	0.421423	−	0.729926i
$35$	−2.25729	−	1.38008i	−0.381552	−	0.233276i
$36$	−2.67884	+	1.35049i	−0.446473	+	0.225081i
$37$	2.40909	+	4.17267i	0.396052	+	0.685983i	0.993235	−	0.116123i	$-0.0370466\pi$
$37$	2.40909	+	4.17267i	0.396052	+	0.685983i	−0.597183	+	0.802105i	$0.703713\pi$
$38$	1.97536	+	3.42143i	0.320446	+	0.555029i
$39$	−5.52715	+	5.22257i	−0.885052	+	0.836281i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−2.29064	−	3.96751i	−0.357738	−	0.619621i	0.629844	−	0.776721i	$-0.283119\pi$
$41$	−2.29064	−	3.96751i	−0.357738	−	0.619621i	−0.987583	+	0.157101i	$0.949785\pi$
$42$	4.48350	−	0.947763i	0.691819	−	0.146243i
$43$	4.90148	−	8.48962i	0.747469	−	1.29465i	−0.201563	−	0.979476i	$-0.564602\pi$
$43$	4.90148	−	8.48962i	0.747469	−	1.29465i	0.949032	−	0.315179i	$-0.102065\pi$
$44$	2.14565	+	3.71637i	0.323469	+	0.560265i
$45$	−0.169863	+	2.99519i	−0.0253216	+	0.446496i
$46$	−0.888355	+	1.53868i	−0.130981	+	0.226866i
$47$	−12.2426			−1.78576			−0.892880	−	0.450294i	$-0.851319\pi$
$47$	−12.2426			−1.78576			−0.892880	+	0.450294i	$0.851319\pi$
$48$	0.400725	+	1.68506i	0.0578396	+	0.243217i
$49$	−6.99115	−	0.351971i	−0.998735	−	0.0502815i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	8.15658	+	2.43514i	1.14215	+	0.340988i
$52$	2.19516	+	3.80213i	0.304414	+	0.527260i
$53$	−4.18972	+	7.25681i	−0.575502	+	0.996799i	0.420484	+	0.907300i	$0.361860\pi$
$53$	−4.18972	+	7.25681i	−0.575502	+	0.996799i	−0.995987	+	0.0894997i	$0.971473\pi$
$54$	−3.34913	−	3.97283i	−0.455759	−	0.540633i
$55$	4.29130			0.578639
$56$	0.0665372	−	2.64491i	0.00889141	−	0.353442i
$57$	−4.97373	+	4.69965i	−0.658786	+	0.622484i
$58$	2.79745	−	4.84532i	0.367323	−	0.636222i
$59$	−11.0744			−1.44177			−0.720884	−	0.693056i	$-0.756264\pi$
$59$	−11.0744			−1.44177			−0.720884	+	0.693056i	$0.756264\pi$
$60$	1.65967	+	0.495491i	0.214262	+	0.0639676i
$61$	−5.47846			−0.701445			−0.350722	−	0.936479i	$-0.614064\pi$
$61$	−5.47846			−0.701445			−0.350722	+	0.936479i	$0.614064\pi$
$62$	−3.53789			−0.449312
$63$	3.39368	+	7.17516i	0.427564	+	0.903985i
$64$	1.00000			0.125000
$65$	4.39032			0.544552
$66$	−5.40249	+	5.10479i	−0.665001	+	0.628356i
$67$	9.14081			1.11673			0.558364	−	0.829596i	$-0.311429\pi$
$67$	9.14081			1.11673			0.558364	+	0.829596i	$0.311429\pi$
$68$	2.45730	−	4.25616i	0.297991	−	0.516136i
$69$	−2.94875	−	0.880345i	−0.354987	−	0.105981i
$70$	−2.25729	−	1.38008i	−0.269798	−	0.164951i
$71$	−4.03887			−0.479325			−0.239663	−	0.970856i	$-0.577037\pi$
$71$	−4.03887			−0.479325			−0.239663	+	0.970856i	$0.577037\pi$
$72$	−2.67884	+	1.35049i	−0.315704	+	0.159157i
$73$	4.69222	−	8.12716i	0.549183	−	0.951212i	−0.449148	−	0.893457i	$-0.648272\pi$
$73$	4.69222	−	8.12716i	0.549183	−	0.951212i	0.998331	−	0.0577550i	$-0.0183942\pi$
$74$	2.40909	+	4.17267i	0.280051	+	0.485063i
$75$	1.25894	−	1.18957i	0.145370	−	0.137359i
$76$	1.97536	+	3.42143i	0.226590	+	0.392465i
$77$	9.97226	−	5.42778i	1.13644	−	0.618553i
$78$	−5.52715	+	5.22257i	−0.625826	+	0.591340i
$79$	−1.10226			−0.124014			−0.0620068	−	0.998076i	$-0.519750\pi$
$79$	−1.10226			−0.124014			−0.0620068	+	0.998076i	$0.519750\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	5.35236	−	7.23548i	0.594707	−	0.803943i
$82$	−2.29064	−	3.96751i	−0.252959	−	0.438138i
$83$	3.33570	−	5.77760i	0.366140	−	0.634174i	−0.622818	−	0.782367i	$-0.714012\pi$
$83$	3.33570	−	5.77760i	0.366140	−	0.634174i	0.988958	+	0.148193i	$0.0473457\pi$
$84$	4.48350	−	0.947763i	0.489190	−	0.103409i
$85$	−2.45730	−	4.25616i	−0.266531	−	0.461646i
$86$	4.90148	−	8.48962i	0.528540	−	0.915459i
$87$	9.28565	+	2.77222i	0.995526	+	0.297213i
$88$	2.14565	+	3.71637i	0.228727	+	0.396167i
$89$	−6.54765	−	11.3409i	−0.694050	−	1.20213i	−0.970500	−	0.241101i	$-0.922491\pi$
$89$	−6.54765	−	11.3409i	−0.694050	−	1.20213i	0.276450	−	0.961028i	$-0.410842\pi$
$90$	−0.169863	+	2.99519i	−0.0179051	+	0.315720i
$91$	10.2024	−	5.55302i	1.06950	−	0.582115i
$92$	−0.888355	+	1.53868i	−0.0926175	+	0.160418i
$93$	−1.41772	−	5.96154i	−0.147011	−	0.618183i
$94$	−12.2426			−1.26272
$95$	3.95072			0.405336
$96$	0.400725	+	1.68506i	0.0408988	+	0.171980i
$97$	0.883722	−	1.53065i	0.0897284	−	0.155414i	−0.817668	−	0.575690i	$-0.804733\pi$
$97$	0.883722	−	1.53065i	0.0897284	−	0.155414i	0.907396	+	0.420276i	$0.138067\pi$
$98$	−6.99115	−	0.351971i	−0.706212	−	0.0355544i
$99$	−10.7668	−	7.05790i	−1.08210	−	0.709345i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−7.78476	−	13.4836i	−0.774613	−	1.34167i	−0.935012	−	0.354616i	$-0.884611\pi$
$101$	−7.78476	−	13.4836i	−0.774613	−	1.34167i	0.160399	−	0.987052i	$-0.448722\pi$
$102$	8.15658	+	2.43514i	0.807622	+	0.241115i
$103$	−8.60051	+	14.8965i	−0.847433	+	1.46780i	0.0360581	+	0.999350i	$0.488520\pi$
$103$	−8.60051	+	14.8965i	−0.847433	+	1.46780i	−0.883491	+	0.468448i	$0.844813\pi$
$104$	2.19516	+	3.80213i	0.215253	+	0.372829i
$105$	1.42096	−	4.35670i	0.138672	−	0.425171i
$106$	−4.18972	+	7.25681i	−0.406942	+	0.704844i
$107$	6.66535	+	11.5447i	0.644364	+	1.11607i	0.984448	+	0.175676i	$0.0562110\pi$
$107$	6.66535	+	11.5447i	0.644364	+	1.11607i	−0.340084	+	0.940395i	$0.610456\pi$
$108$	−3.34913	−	3.97283i	−0.322270	−	0.382285i
$109$	1.19326	−	2.06678i	0.114293	−	0.197962i	−0.803204	−	0.595704i	$-0.796873\pi$
$109$	1.19326	−	2.06678i	0.114293	−	0.197962i	0.917497	+	0.397743i	$0.130206\pi$
$110$	4.29130			0.409159
$111$	−6.06581	+	5.73155i	−0.575741	+	0.544015i
$112$	0.0665372	−	2.64491i	0.00628718	−	0.249921i
$113$	−3.10974	−	5.38623i	−0.292540	−	0.506694i	0.681870	−	0.731474i	$-0.261167\pi$
$113$	−3.10974	−	5.38623i	−0.292540	−	0.506694i	−0.974410	+	0.224780i	$0.927834\pi$
$114$	−4.97373	+	4.69965i	−0.465832	+	0.440162i
$115$	0.888355	+	1.53868i	0.0828396	+	0.143482i
$116$	2.79745	−	4.84532i	0.259736	−	0.449877i
$117$	−11.0152	−	7.22075i	−1.01836	−	0.667559i
$118$	−11.0744			−1.01948
$119$	−11.0937	−	6.78253i	−1.01696	−	0.621754i
$120$	1.65967	+	0.495491i	0.151506	+	0.0452320i
$121$	−3.70763	+	6.42180i	−0.337057	+	0.583800i
$122$	−5.47846			−0.495996
$123$	5.76756	−	5.44974i	0.520044	−	0.491387i
$124$	−3.53789			−0.317712
$125$	−1.00000			−0.0894427
$126$	3.39368	+	7.17516i	0.302333	+	0.639214i
$127$	4.92903			0.437381			0.218691	−	0.975794i	$-0.429821\pi$
$127$	4.92903			0.437381			0.218691	+	0.975794i	$0.429821\pi$
$128$	1.00000			0.0883883
$129$	16.2696	+	4.85728i	1.43246	+	0.427660i
$130$	4.39032			0.385056
$131$	6.71245	−	11.6263i	0.586470	−	1.01580i	−0.408221	−	0.912883i	$-0.633851\pi$
$131$	6.71245	−	11.6263i	0.586470	−	1.01580i	0.994690	−	0.102912i	$-0.0328161\pi$
$132$	−5.40249	+	5.10479i	−0.470227	+	0.444315i
$133$	9.18082	−	4.99701i	0.796078	−	0.433296i
$134$	9.14081			0.789645
$135$	−5.11513	+	0.914017i	−0.440240	+	0.0786660i
$136$	2.45730	−	4.25616i	0.210711	−	0.364963i
$137$	−5.91661	−	10.2479i	−0.505490	−	0.875534i	−0.999980	−	0.00635092i	$-0.997978\pi$
$137$	−5.91661	−	10.2479i	−0.505490	−	0.875534i	0.494490	−	0.869183i	$-0.335355\pi$
$138$	−2.94875	−	0.880345i	−0.251014	−	0.0749399i
$139$	1.90549	+	3.30041i	0.161622	+	0.279937i	0.935450	−	0.353458i	$-0.114994\pi$
$139$	1.90549	+	3.30041i	0.161622	+	0.279937i	−0.773829	+	0.633395i	$0.781661\pi$
$140$	−2.25729	−	1.38008i	−0.190776	−	0.116638i
$141$	−4.90589	−	20.6294i	−0.413151	−	1.73731i
$142$	−4.03887			−0.338934
$143$	−9.42008	+	16.3161i	−0.787747	+	1.36442i
$144$	−2.67884	+	1.35049i	−0.223237	+	0.112541i
$145$	−2.79745	−	4.84532i	−0.232315	−	0.402382i
$146$	4.69222	−	8.12716i	0.388331	−	0.672609i
$147$	−2.20843	−	11.9215i	−0.182149	−	0.983271i
$148$	2.40909	+	4.17267i	0.198026	+	0.342991i
$149$	−4.50969	+	7.81101i	−0.369448	+	0.639903i	−0.989479	−	0.144674i	$-0.953787\pi$
$149$	−4.50969	+	7.81101i	−0.369448	+	0.639903i	0.620031	+	0.784577i	$0.287120\pi$
$150$	1.25894	−	1.18957i	0.102792	−	0.0971277i
$151$	6.92316	+	11.9913i	0.563399	+	0.975836i	0.997197	+	0.0748255i	$0.0238400\pi$
$151$	6.92316	+	11.9913i	0.563399	+	0.975836i	−0.433798	+	0.901010i	$0.642827\pi$
$152$	1.97536	+	3.42143i	0.160223	+	0.277514i
$153$	−0.834806	+	14.7201i	−0.0674901	+	1.19005i
$154$	9.97226	−	5.42778i	0.803588	−	0.437383i
$155$	−1.76894	+	3.06390i	−0.142085	+	0.246098i
$156$	−5.52715	+	5.22257i	−0.442526	+	0.418141i
$157$	21.0517			1.68011			0.840055	−	0.542501i	$-0.182523\pi$
$157$	21.0517			1.68011			0.840055	+	0.542501i	$0.182523\pi$
$158$	−1.10226			−0.0876909
$159$	−13.9071	−	4.15194i	−1.10290	−	0.329270i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	4.01056	+	2.45200i	0.316076	+	0.193245i
$162$	5.35236	−	7.23548i	0.420521	−	0.568473i
$163$	2.03798	+	3.52989i	0.159627	+	0.276482i	0.934734	−	0.355348i	$-0.115638\pi$
$163$	2.03798	+	3.52989i	0.159627	+	0.276482i	−0.775107	+	0.631830i	$0.782304\pi$
$164$	−2.29064	−	3.96751i	−0.178869	−	0.309810i
$165$	1.71963	+	7.23109i	0.133873	+	0.562939i
$166$	3.33570	−	5.77760i	0.258900	−	0.448429i
$167$	9.22182	+	15.9727i	0.713606	+	1.23600i	0.963495	+	0.267727i	$0.0862727\pi$
$167$	9.22182	+	15.9727i	0.713606	+	1.23600i	−0.249889	+	0.968275i	$0.580394\pi$
$168$	4.48350	−	0.947763i	0.345909	−	0.0731215i
$169$	−3.13744	+	5.43421i	−0.241342	+	0.418016i
$170$	−2.45730	−	4.25616i	−0.188466	−	0.326433i
$171$	−9.91227	−	6.49775i	−0.758011	−	0.496895i
$172$	4.90148	−	8.48962i	0.373735	−	0.647327i
$173$	−18.8642			−1.43422			−0.717109	−	0.696961i	$-0.754535\pi$
$173$	−18.8642			−1.43422			−0.717109	+	0.696961i	$0.754535\pi$
$174$	9.28565	+	2.77222i	0.703943	+	0.210162i
$175$	−2.32383	+	1.26483i	−0.175665	+	0.0956125i
$176$	2.14565	+	3.71637i	0.161734	+	0.280132i
$177$	−4.43780	−	18.6611i	−0.333565	−	1.40265i
$178$	−6.54765	−	11.3409i	−0.490767	−	0.850034i
$179$	−6.79281	+	11.7655i	−0.507719	+	0.879395i	0.492241	+	0.870459i	$0.336178\pi$
$179$	−6.79281	+	11.7655i	−0.507719	+	0.879395i	−0.999960	+	0.00893589i	$0.997156\pi$
$180$	−0.169863	+	2.99519i	−0.0126608	+	0.223248i
$181$	−22.4169			−1.66623			−0.833116	−	0.553099i	$-0.813445\pi$
$181$	−22.4169			−1.66623			−0.833116	+	0.553099i	$0.813445\pi$
$182$	10.2024	−	5.55302i	0.756249	−	0.411618i
$183$	−2.19535	−	9.23152i	−0.162285	−	0.682414i
$184$	−0.888355	+	1.53868i	−0.0654904	+	0.113433i
$185$	4.81818			0.354240
$186$	−1.41772	−	5.96154i	−0.103952	−	0.437122i
$187$	21.0900			1.54225
$188$	−12.2426			−0.892880
$189$	−10.7306	+	8.59382i	−0.780538	+	0.625108i
$190$	3.95072			0.286616
$191$	7.02722			0.508472			0.254236	−	0.967142i	$-0.418176\pi$
$191$	7.02722			0.508472			0.254236	+	0.967142i	$0.418176\pi$
$192$	0.400725	+	1.68506i	0.0289198	+	0.121609i
$193$	3.28486			0.236449			0.118225	−	0.992987i	$-0.462280\pi$
$193$	3.28486			0.236449			0.118225	+	0.992987i	$0.462280\pi$
$194$	0.883722	−	1.53065i	0.0634475	−	0.109894i
$195$	1.75931	+	7.39794i	0.125987	+	0.529777i
$196$	−6.99115	−	0.351971i	−0.499368	−	0.0251408i
$197$	3.44482			0.245433			0.122717	−	0.992442i	$-0.460839\pi$
$197$	3.44482			0.245433			0.122717	+	0.992442i	$0.460839\pi$
$198$	−10.7668	−	7.05790i	−0.765161	−	0.501583i
$199$	−8.91802	+	15.4465i	−0.632181	+	1.09497i	0.354923	+	0.934895i	$0.384507\pi$
$199$	−8.91802	+	15.4465i	−0.632181	+	1.09497i	−0.987105	+	0.160075i	$0.948826\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	3.66295	+	15.4028i	0.258364	+	1.08643i
$202$	−7.78476	−	13.4836i	−0.547734	−	0.948703i
$203$	−12.6293	−	7.72140i	−0.886405	−	0.541936i
$204$	8.15658	+	2.43514i	0.571075	+	0.170494i
$205$	−4.58128			−0.319971
$206$	−8.60051	+	14.8965i	−0.599226	+	1.03789i
$207$	0.301797	−	5.32158i	0.0209763	−	0.369876i
$208$	2.19516	+	3.80213i	0.152207	+	0.263630i
$209$	−8.47687	+	14.6824i	−0.586357	+	1.01560i
$210$	1.42096	−	4.35670i	0.0980557	−	0.300641i
$211$	9.52036	+	16.4897i	0.655409	+	1.13520i	0.981791	+	0.189963i	$0.0608369\pi$
$211$	9.52036	+	16.4897i	0.655409	+	1.13520i	−0.326383	+	0.945238i	$0.605830\pi$
$212$	−4.18972	+	7.25681i	−0.287751	+	0.498400i
$213$	−1.61847	−	6.80572i	−0.110896	−	0.466320i
$214$	6.66535	+	11.5447i	0.455634	+	0.789181i
$215$	−4.90148	−	8.48962i	−0.334278	−	0.578987i
$216$	−3.34913	−	3.97283i	−0.227879	−	0.270317i
$217$	−0.235401	+	9.35741i	−0.0159801	+	0.635222i
$218$	1.19326	−	2.06678i	0.0808175	−	0.139980i
$219$	15.5750	+	4.64991i	1.05246	+	0.314212i
$220$	4.29130			0.289319
$221$	21.5766			1.45140
$222$	−6.06581	+	5.73155i	−0.407110	+	0.384676i
$223$	9.77058	−	16.9231i	0.654286	−	1.13326i	−0.327786	−	0.944752i	$-0.606302\pi$
$223$	9.77058	−	16.9231i	0.654286	−	1.13326i	0.982072	−	0.188505i	$-0.0603642\pi$
$224$	0.0665372	−	2.64491i	0.00444571	−	0.176721i
$225$	2.50898	+	1.64470i	0.167265	+	0.109647i
$226$	−3.10974	−	5.38623i	−0.206857	−	0.358287i
$227$	2.49678	+	4.32454i	0.165717	+	0.287030i	0.936910	−	0.349572i	$-0.113673\pi$
$227$	2.49678	+	4.32454i	0.165717	+	0.287030i	−0.771193	+	0.636602i	$0.780340\pi$
$228$	−4.97373	+	4.69965i	−0.329393	+	0.311242i
$229$	−2.25929	+	3.91321i	−0.149298	+	0.258592i	−0.930968	−	0.365100i	$-0.881035\pi$
$229$	−2.25929	+	3.91321i	−0.149298	+	0.258592i	0.781670	+	0.623692i	$0.214368\pi$
$230$	0.888355	+	1.53868i	0.0585764	+	0.101457i
$231$	13.1423	+	14.6288i	0.864697	+	0.962504i
$232$	2.79745	−	4.84532i	0.183661	−	0.318111i
$233$	−10.8333	−	18.7639i	−0.709714	−	1.22926i	−0.964963	−	0.262386i	$-0.915491\pi$
$233$	−10.8333	−	18.7639i	−0.709714	−	1.22926i	0.255249	−	0.966875i	$-0.417843\pi$
$234$	−11.0152	−	7.22075i	−0.720086	−	0.472035i
$235$	−6.12128	+	10.6024i	−0.399308	+	0.691622i
$236$	−11.0744			−0.720884
$237$	−0.441702	−	1.85737i	−0.0286916	−	0.120649i
$238$	−11.0937	−	6.78253i	−0.719097	−	0.439646i
$239$	−7.21014	−	12.4883i	−0.466385	−	0.807802i	0.532878	−	0.846192i	$-0.321111\pi$
$239$	−7.21014	−	12.4883i	−0.466385	−	0.807802i	−0.999263	+	0.0383897i	$0.987777\pi$
$240$	1.65967	+	0.495491i	0.107131	+	0.0319838i
$241$	−3.04065	−	5.26656i	−0.195866	−	0.339249i	0.751318	−	0.659940i	$-0.229418\pi$
$241$	−3.04065	−	5.26656i	−0.195866	−	0.339249i	−0.947184	+	0.320691i	$0.896085\pi$
$242$	−3.70763	+	6.42180i	−0.238335	+	0.412809i
$243$	14.3370	+	6.11961i	0.919721	+	0.392573i
$244$	−5.47846			−0.350722
$245$	−3.80039	+	5.87852i	−0.242798	+	0.375565i
$246$	5.76756	−	5.44974i	0.367726	−	0.347463i
$247$	−8.67247	+	15.0212i	−0.551816	+	0.955773i
$248$	−3.53789			−0.224656
$249$	11.0723	+	3.30562i	0.701677	+	0.209485i
$250$	−1.00000			−0.0632456
$251$	−0.0471320			−0.00297495			−0.00148747	−	0.999999i	$-0.500473\pi$
$251$	−0.0471320			−0.00297495			−0.00148747	+	0.999999i	$0.500473\pi$
$252$	3.39368	+	7.17516i	0.213782	+	0.451993i
$253$	−7.62440			−0.479342
$254$	4.92903			0.309275
$255$	6.18718	−	5.84624i	0.387456	−	0.366106i
$256$	1.00000			0.0625000
$257$	−0.867267	+	1.50215i	−0.0540986	+	0.0937016i	−0.891807	−	0.452417i	$-0.850562\pi$
$257$	−0.867267	+	1.50215i	−0.0540986	+	0.0937016i	0.837708	+	0.546119i	$0.183895\pi$
$258$	16.2696	+	4.85728i	1.01290	+	0.302401i
$259$	11.1966	−	6.09420i	0.695726	−	0.378675i
$260$	4.39032			0.272276
$261$	−0.950364	+	16.7578i	−0.0588260	+	1.03728i
$262$	6.71245	−	11.6263i	0.414697	−	0.718276i
$263$	−6.53435	−	11.3178i	−0.402925	−	0.697887i	0.591152	−	0.806560i	$-0.298673\pi$
$263$	−6.53435	−	11.3178i	−0.402925	−	0.697887i	−0.994078	+	0.108673i	$0.965340\pi$
$264$	−5.40249	+	5.10479i	−0.332500	+	0.314178i
$265$	4.18972	+	7.25681i	0.257373	+	0.445782i
$266$	9.18082	−	4.99701i	0.562912	−	0.306386i
$267$	16.4862	−	15.5777i	1.00894	−	0.953342i
$268$	9.14081			0.558364
$269$	−10.0426	+	17.3942i	−0.612306	+	1.06054i	0.378545	+	0.925583i	$0.376424\pi$
$269$	−10.0426	+	17.3942i	−0.612306	+	1.06054i	−0.990851	+	0.134961i	$0.956909\pi$
$270$	−5.11513	+	0.914017i	−0.311297	+	0.0556253i
$271$	−3.48267	−	6.03216i	−0.211557	−	0.366427i	0.740645	−	0.671897i	$-0.234520\pi$
$271$	−3.48267	−	6.03216i	−0.211557	−	0.366427i	−0.952202	+	0.305469i	$0.901187\pi$
$272$	2.45730	−	4.25616i	0.148995	−	0.258068i
$273$	13.4455	+	14.9663i	0.813759	+	0.905804i
$274$	−5.91661	−	10.2479i	−0.357435	−	0.619096i
$275$	2.14565	−	3.71637i	0.129388	−	0.224106i
$276$	−2.94875	−	0.880345i	−0.177494	−	0.0529905i
$277$	6.55182	+	11.3481i	0.393661	+	0.681840i	0.992929	−	0.118708i	$-0.0378752\pi$
$277$	6.55182	+	11.3481i	0.393661	+	0.681840i	−0.599269	+	0.800548i	$0.704542\pi$
$278$	1.90549	+	3.30041i	0.114284	+	0.197946i
$279$	9.47743	−	4.77787i	0.567399	−	0.286044i
$280$	−2.25729	−	1.38008i	−0.134899	−	0.0824756i
$281$	10.0445	−	17.3975i	0.599202	−	1.03785i	−0.393737	−	0.919223i	$-0.628818\pi$
$281$	10.0445	−	17.3975i	0.599202	−	1.03785i	0.992939	−	0.118626i	$-0.0378488\pi$
$282$	−4.90589	−	20.6294i	−0.292142	−	1.22846i
$283$	7.90498			0.469902			0.234951	−	0.972007i	$-0.424507\pi$
$283$	7.90498			0.469902			0.234951	+	0.972007i	$0.424507\pi$
$284$	−4.03887			−0.239663
$285$	1.58315	+	6.65720i	0.0937778	+	0.394338i
$286$	−9.42008	+	16.3161i	−0.557021	+	0.964789i
$287$	−10.6461	+	5.79457i	−0.628421	+	0.342042i
$288$	−2.67884	+	1.35049i	−0.157852	+	0.0795783i
$289$	−3.57661	−	6.19488i	−0.210389	−	0.364405i
$290$	−2.79745	−	4.84532i	−0.164272	−	0.284527i
$291$	2.93336	+	0.875753i	0.171957	+	0.0513375i
$292$	4.69222	−	8.12716i	0.274591	−	0.475606i
$293$	14.8537	+	25.7273i	0.867761	+	1.50301i	0.864280	+	0.503011i	$0.167775\pi$
$293$	14.8537	+	25.7273i	0.867761	+	1.50301i	0.00348076	+	0.999994i	$0.498892\pi$
$294$	−2.20843	−	11.9215i	−0.128798	−	0.695278i
$295$	−5.53721	+	9.59074i	−0.322389	+	0.558394i
$296$	2.40909	+	4.17267i	0.140026	+	0.242532i
$297$	7.57845	−	20.9709i	0.439746	−	1.21686i
$298$	−4.50969	+	7.81101i	−0.261239	+	0.452479i
$299$	−7.80032			−0.451104
$300$	1.25894	−	1.18957i	0.0726850	−	0.0686797i
$301$	−22.1282	−	13.5289i	−1.27545	−	0.779792i
$302$	6.92316	+	11.9913i	0.398383	+	0.690020i
$303$	19.6011	−	18.5210i	1.12605	−	1.06400i
$304$	1.97536	+	3.42143i	0.113295	+	0.196232i
$305$	−2.73923	+	4.74448i	−0.156848	+	0.271668i
$306$	−0.834806	+	14.7201i	−0.0477227	+	0.841494i
$307$	−12.9068			−0.736630			−0.368315	−	0.929701i	$-0.620065\pi$
$307$	−12.9068			−0.736630			−0.368315	+	0.929701i	$0.620065\pi$
$308$	9.97226	−	5.42778i	0.568222	−	0.309277i
$309$	−28.5479	−	8.52295i	−1.62403	−	0.484854i
$310$	−1.76894	+	3.06390i	−0.100469	+	0.174018i
$311$	17.5015			0.992417			0.496208	−	0.868203i	$-0.334725\pi$
$311$	17.5015			0.992417			0.496208	+	0.868203i	$0.334725\pi$
$312$	−5.52715	+	5.22257i	−0.312913	+	0.295670i
$313$	32.8823			1.85862			0.929309	−	0.369302i	$-0.120403\pi$
$313$	32.8823			1.85862			0.929309	+	0.369302i	$0.120403\pi$
$314$	21.0517			1.18802
$315$	7.91071	+	0.648564i	0.445718	+	0.0365424i
$316$	−1.10226			−0.0620068
$317$	4.00696			0.225053			0.112527	−	0.993649i	$-0.464106\pi$
$317$	4.00696			0.225053			0.112527	+	0.993649i	$0.464106\pi$
$318$	−13.9071	−	4.15194i	−0.779870	−	0.232829i
$319$	24.0094			1.34427
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−16.7826	+	15.8578i	−0.936711	+	0.885094i
$322$	4.01056	+	2.45200i	0.223500	+	0.136645i
$323$	19.4162			1.08035
$324$	5.35236	−	7.23548i	0.297354	−	0.401971i
$325$	2.19516	−	3.80213i	0.121765	−	0.210904i
$326$	2.03798	+	3.52989i	0.112873	+	0.195502i
$327$	3.96081	+	1.18250i	0.219033	+	0.0653922i
$328$	−2.29064	−	3.96751i	−0.126480	−	0.219069i
$329$	−0.814586	+	32.3805i	−0.0449096	+	1.78520i
$330$	1.71963	+	7.23109i	0.0946625	+	0.398058i
$331$	−35.3089			−1.94075			−0.970375	−	0.241602i	$-0.922327\pi$
$331$	−35.3089			−1.94075			−0.970375	+	0.241602i	$0.922327\pi$
$332$	3.33570	−	5.77760i	0.183070	−	0.317087i
$333$	−12.0887	−	7.92446i	−0.662457	−	0.434258i
$334$	9.22182	+	15.9727i	0.504596	+	0.873985i
$335$	4.57040	−	7.91617i	0.249708	−	0.432507i
$336$	4.48350	−	0.947763i	0.244595	−	0.0517047i
$337$	−14.0339	−	24.3074i	−0.764474	−	1.32411i	−0.940524	−	0.339726i	$-0.889666\pi$
$337$	−14.0339	−	24.3074i	−0.764474	−	1.32411i	0.176050	−	0.984381i	$-0.443668\pi$
$338$	−3.13744	+	5.43421i	−0.170654	+	0.295582i
$339$	7.82996	−	7.39849i	0.425265	−	0.401831i
$340$	−2.45730	−	4.25616i	−0.133266	−	0.230823i
$341$	−7.59107	−	13.1481i	−0.411079	−	0.712010i
$342$	−9.91227	−	6.49775i	−0.535994	−	0.351358i
$343$	−1.39610	+	18.4676i	−0.0753825	+	0.997155i
$344$	4.90148	−	8.48962i	0.264270	−	0.457729i
$345$	−2.23677	+	2.11352i	−0.120424	+	0.113788i
$346$	−18.8642			−1.01415
$347$	17.6505			0.947527			0.473763	−	0.880652i	$-0.342895\pi$
$347$	17.6505			0.947527			0.473763	+	0.880652i	$0.342895\pi$
$348$	9.28565	+	2.77222i	0.497763	+	0.148607i
$349$	7.74918	−	13.4220i	0.414804	−	0.718462i	−0.580604	−	0.814186i	$-0.697183\pi$
$349$	7.74918	−	13.4220i	0.414804	−	0.718462i	0.995408	+	0.0957245i	$0.0305168\pi$
$350$	−2.32383	+	1.26483i	−0.124214	+	0.0676082i
$351$	7.75332	−	21.4548i	0.413842	−	1.14517i
$352$	2.14565	+	3.71637i	0.114364	+	0.198083i
$353$	−4.88224	−	8.45629i	−0.259855	−	0.450083i	0.706348	−	0.707865i	$-0.250342\pi$
$353$	−4.88224	−	8.45629i	−0.259855	−	0.450083i	−0.966203	+	0.257782i	$0.917008\pi$
$354$	−4.43780	−	18.6611i	−0.235866	−	0.991824i
$355$	−2.01943	+	3.49776i	−0.107180	+	0.185642i
$356$	−6.54765	−	11.3409i	−0.347025	−	0.601065i
$357$	6.98345	−	21.4114i	0.369603	−	1.13321i
$358$	−6.79281	+	11.7655i	−0.359011	+	0.621826i
$359$	8.43793	+	14.6149i	0.445337	+	0.771346i	0.998076	−	0.0620086i	$-0.0197506\pi$
$359$	8.43793	+	14.6149i	0.445337	+	0.771346i	−0.552739	+	0.833355i	$0.686417\pi$
$360$	−0.169863	+	2.99519i	−0.00895255	+	0.157860i
$361$	1.69589	−	2.93737i	0.0892574	−	0.154598i
$362$	−22.4169			−1.17820
$363$	−12.3068	−	3.67419i	−0.645942	−	0.192845i
$364$	10.2024	−	5.55302i	0.534749	−	0.291058i
$365$	−4.69222	−	8.12716i	−0.245602	−	0.425395i
$366$	−2.19535	−	9.23152i	−0.114753	−	0.482539i
$367$	3.80501	+	6.59048i	0.198620	+	0.344020i	0.948081	−	0.318028i	$-0.103021\pi$
$367$	3.80501	+	6.59048i	0.198620	+	0.344020i	−0.749461	+	0.662048i	$0.769687\pi$
$368$	−0.888355	+	1.53868i	−0.0463087	+	0.0802091i
$369$	11.4943	+	7.53483i	0.598371	+	0.392248i
$370$	4.81818			0.250485
$371$	18.9149	+	11.5643i	0.982011	+	0.600389i
$372$	−1.41772	−	5.96154i	−0.0735053	−	0.309092i
$373$	5.46643	−	9.46813i	0.283041	−	0.490241i	−0.689091	−	0.724675i	$-0.741990\pi$
$373$	5.46643	−	9.46813i	0.283041	−	0.490241i	0.972132	+	0.234433i	$0.0753234\pi$
$374$	21.0900			1.09054
$375$	−0.400725	−	1.68506i	−0.0206933	−	0.0870160i
$376$	−12.2426			−0.631362
$377$	24.5634			1.26508
$378$	−10.7306	+	8.59382i	−0.551924	+	0.442018i
$379$	−15.9380			−0.818678			−0.409339	−	0.912382i	$-0.634241\pi$
$379$	−15.9380			−0.818678			−0.409339	+	0.912382i	$0.634241\pi$
$380$	3.95072			0.202668
$381$	1.97519	+	8.30571i	0.101192	+	0.425514i
$382$	7.02722			0.359544
$383$	3.36190	−	5.82298i	0.171785	−	0.297541i	−0.767259	−	0.641338i	$-0.778380\pi$
$383$	3.36190	−	5.82298i	0.171785	−	0.297541i	0.939044	+	0.343797i	$0.111713\pi$
$384$	0.400725	+	1.68506i	0.0204494	+	0.0859902i
$385$	0.285531	−	11.3501i	0.0145520	−	0.578456i
$386$	3.28486			0.167195
$387$	−1.66516	+	29.3617i	−0.0846447	+	1.49254i
$388$	0.883722	−	1.53065i	0.0448642	−	0.0777070i
$389$	4.52819	+	7.84305i	0.229588	+	0.397658i	0.957686	−	0.287815i	$-0.0929287\pi$
$389$	4.52819	+	7.84305i	0.229588	+	0.397658i	−0.728098	+	0.685473i	$0.759595\pi$
$390$	1.75931	+	7.39794i	0.0890860	+	0.374609i
$391$	4.36591	+	7.56197i	0.220793	+	0.382425i
$392$	−6.99115	−	0.351971i	−0.353106	−	0.0177772i
$393$	22.2809	+	6.65192i	1.12392	+	0.335545i
$394$	3.44482			0.173548
$395$	−0.551129	+	0.954583i	−0.0277303	+	0.0480303i
$396$	−10.7668	−	7.05790i	−0.541051	−	0.354673i
$397$	16.9811	+	29.4122i	0.852258	+	1.47615i	0.879165	+	0.476517i	$0.158101\pi$
$397$	16.9811	+	29.4122i	0.852258	+	1.47615i	−0.0269071	+	0.999638i	$0.508566\pi$
$398$	−8.91802	+	15.4465i	−0.447020	+	0.774261i
$399$	12.0992	+	13.4678i	0.605719	+	0.674232i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−15.3883	+	26.6533i	−0.768454	+	1.33100i	0.169947	+	0.985453i	$0.445640\pi$
$401$	−15.3883	+	26.6533i	−0.768454	+	1.33100i	−0.938401	+	0.345548i	$0.887693\pi$
$402$	3.66295	+	15.4028i	0.182691	+	0.768221i
$403$	−7.76622	−	13.4515i	−0.386863	−	0.670067i
$404$	−7.78476	−	13.4836i	−0.387306	−	0.670834i
$405$	−3.58993	−	8.25302i	−0.178385	−	0.410096i
$406$	−12.6293	−	7.72140i	−0.626783	−	0.383207i
$407$	−10.3381	+	17.9062i	−0.512442	+	0.887576i
$408$	8.15658	+	2.43514i	0.403811	+	0.120557i
$409$	−12.7154			−0.628738			−0.314369	−	0.949301i	$-0.601793\pi$
$409$	−12.7154			−0.628738			−0.314369	+	0.949301i	$0.601793\pi$
$410$	−4.58128			−0.226254
$411$	14.8973	−	14.0764i	0.734830	−	0.694338i
$412$	−8.60051	+	14.8965i	−0.423717	+	0.733899i
$413$	−0.736862	+	29.2909i	−0.0362586	+	1.44131i
$414$	0.301797	−	5.32158i	0.0148325	−	0.261541i
$415$	−3.33570	−	5.77760i	−0.163743	−	0.283611i
$416$	2.19516	+	3.80213i	0.107627	+	0.186415i
$417$	−4.79781	+	4.53342i	−0.234950	+	0.222003i
$418$	−8.47687	+	14.6824i	−0.414617	+	0.718138i
$419$	4.84388	+	8.38985i	0.236639	+	0.409871i	0.959748	−	0.280863i	$-0.0906207\pi$
$419$	4.84388	+	8.38985i	0.236639	+	0.409871i	−0.723109	+	0.690734i	$0.757287\pi$
$420$	1.42096	−	4.35670i	0.0693358	−	0.212585i
$421$	−14.3536	+	24.8611i	−0.699551	+	1.21166i	0.269072	+	0.963120i	$0.413283\pi$
$421$	−14.3536	+	24.8611i	−0.699551	+	1.21166i	−0.968622	+	0.248537i	$0.920050\pi$
$422$	9.52036	+	16.4897i	0.463444	+	0.802708i
$423$	32.7959	−	16.5334i	1.59459	−	0.803883i
$424$	−4.18972	+	7.25681i	−0.203471	+	0.352422i
$425$	−4.91459			−0.238393
$426$	−1.61847	−	6.80572i	−0.0784153	−	0.329738i
$427$	−0.364522	+	14.4901i	−0.0176404	+	0.701223i
$428$	6.66535	+	11.5447i	0.322182	+	0.558035i
$429$	−31.2684	−	9.33514i	−1.50965	−	0.450705i
$430$	−4.90148	−	8.48962i	−0.236370	−	0.409406i
$431$	3.62516	−	6.27897i	0.174618	−	0.302447i	−0.765411	−	0.643542i	$-0.777464\pi$
$431$	3.62516	−	6.27897i	0.174618	−	0.302447i	0.940029	+	0.341095i	$0.110798\pi$
$432$	−3.34913	−	3.97283i	−0.161135	−	0.191143i
$433$	−18.8871			−0.907654			−0.453827	−	0.891090i	$-0.649942\pi$
$433$	−18.8871			−0.907654			−0.453827	+	0.891090i	$0.649942\pi$
$434$	−0.235401	+	9.35741i	−0.0112996	+	0.449170i
$435$	7.04364	−	6.65550i	0.337717	−	0.319107i
$436$	1.19326	−	2.06678i	0.0571466	−	0.0989808i
$437$	−7.01929			−0.335778
$438$	15.5750	+	4.64991i	0.744204	+	0.222181i
$439$	2.09125			0.0998101			0.0499051	−	0.998754i	$-0.484108\pi$
$439$	2.09125			0.0998101			0.0499051	+	0.998754i	$0.484108\pi$
$440$	4.29130			0.204580
$441$	19.2035	−	8.49859i	0.914452	−	0.404695i
$442$	21.5766			1.02630
$443$	−11.8707			−0.563992			−0.281996	−	0.959416i	$-0.590997\pi$
$443$	−11.8707			−0.563992			−0.281996	+	0.959416i	$0.590997\pi$
$444$	−6.06581	+	5.73155i	−0.287870	+	0.272007i
$445$	−13.0953			−0.620777
$446$	9.77058	−	16.9231i	0.462650	−	0.801334i
$447$	−14.9691	−	4.46902i	−0.708016	−	0.211377i
$448$	0.0665372	−	2.64491i	0.00314359	−	0.124960i
$449$	21.7279			1.02540			0.512700	−	0.858568i	$-0.328645\pi$
$449$	21.7279			1.02540			0.512700	+	0.858568i	$0.328645\pi$
$450$	2.50898	+	1.64470i	0.118274	+	0.0775319i
$451$	9.82983	−	17.0258i	0.462869	−	0.801712i
$452$	−3.10974	−	5.38623i	−0.146270	−	0.253347i
$453$	−17.4317	+	16.4711i	−0.819013	+	0.773881i
$454$	2.49678	+	4.32454i	0.117180	+	0.202961i
$455$	0.292120	−	11.6120i	0.0136948	−	0.544380i
$456$	−4.97373	+	4.69965i	−0.232916	+	0.220081i
$457$	6.44326			0.301403			0.150701	−	0.988579i	$-0.451847\pi$
$457$	6.44326			0.301403			0.150701	+	0.988579i	$0.451847\pi$
$458$	−2.25929	+	3.91321i	−0.105570	+	0.182852i
$459$	−25.1388	+	4.49202i	−1.17338	+	0.209670i
$460$	0.888355	+	1.53868i	0.0414198	+	0.0717412i
$461$	−0.496819	+	0.860516i	−0.0231392	+	0.0400782i	−0.877363	−	0.479827i	$-0.840699\pi$
$461$	−0.496819	+	0.860516i	−0.0231392	+	0.0400782i	0.854224	+	0.519905i	$0.174033\pi$
$462$	13.1423	+	14.6288i	0.611433	+	0.680593i
$463$	8.98000	+	15.5538i	0.417336	+	0.722847i	0.995671	−	0.0929527i	$-0.0296306\pi$
$463$	8.98000	+	15.5538i	0.417336	+	0.722847i	−0.578335	+	0.815800i	$0.696297\pi$
$464$	2.79745	−	4.84532i	0.129868	−	0.224938i
$465$	−5.87171	−	1.75299i	−0.272294	−	0.0812931i
$466$	−10.8333	−	18.7639i	−0.501844	−	0.869219i
$467$	0.111695	+	0.193461i	0.00516863	+	0.00895232i	0.868598	−	0.495517i	$-0.165021\pi$
$467$	0.111695	+	0.193461i	0.00516863	+	0.00895232i	−0.863430	+	0.504469i	$0.831688\pi$
$468$	−11.0152	−	7.22075i	−0.509178	−	0.333779i
$469$	0.608204	−	24.1767i	0.0280843	−	1.11637i
$470$	−6.12128	+	10.6024i	−0.282354	+	0.489051i
$471$	8.43594	+	35.4734i	0.388708	+	1.63453i
$472$	−11.0744			−0.509742
$473$	42.0675			1.93426
$474$	−0.441702	−	1.85737i	−0.0202880	−	0.0853117i
$475$	1.97536	−	3.42143i	0.0906358	−	0.156986i
$476$	−11.0937	−	6.78253i	−0.508478	−	0.310877i
$477$	1.42335	−	25.0980i	0.0651709	−	1.14916i
$478$	−7.21014	−	12.4883i	−0.329784	−	0.571203i
$479$	0.610293	+	1.05706i	0.0278850	+	0.0482983i	0.879631	−	0.475656i	$-0.157789\pi$
$479$	0.610293	+	1.05706i	0.0278850	+	0.0482983i	−0.851746	+	0.523955i	$0.824456\pi$
$480$	1.65967	+	0.495491i	0.0757530	+	0.0226160i
$481$	−10.5767	+	18.3193i	−0.482255	+	0.835290i
$482$	−3.04065	−	5.26656i	−0.138498	−	0.239885i
$483$	−2.52464	+	7.74060i	−0.114875	+	0.352210i
$484$	−3.70763	+	6.42180i	−0.168529	+	0.291900i
$485$	−0.883722	−	1.53065i	−0.0401277	−	0.0695033i
$486$	14.3370	+	6.11961i	0.650341	+	0.277591i
$487$	−19.6408	+	34.0188i	−0.890008	+	1.54154i	−0.0501447	+	0.998742i	$0.515968\pi$
$487$	−19.6408	+	34.0188i	−0.890008	+	1.54154i	−0.839864	+	0.542798i	$0.817365\pi$
$488$	−5.47846			−0.247998
$489$	−5.13139	+	4.84863i	−0.232050	+	0.219263i
$490$	−3.80039	+	5.87852i	−0.171684	+	0.265565i
$491$	4.41619	+	7.64907i	0.199300	+	0.345198i	0.948302	−	0.317370i	$-0.102800\pi$
$491$	4.41619	+	7.64907i	0.199300	+	0.345198i	−0.749002	+	0.662568i	$0.769467\pi$
$492$	5.76756	−	5.44974i	0.260022	−	0.245693i
$493$	−13.7483	−	23.8128i	−0.619193	−	1.07247i
$494$	−8.67247	+	15.0212i	−0.390193	+	0.675834i
$495$	−11.4957	+	5.79535i	−0.516693	+	0.260482i
$496$	−3.53789			−0.158856
$497$	−0.268735	+	10.6825i	−0.0120544	+	0.479174i
$498$	11.0723	+	3.30562i	0.496161	+	0.148128i
$499$	18.7710	−	32.5123i	0.840306	−	1.45545i	−0.0493305	−	0.998783i	$-0.515709\pi$
$499$	18.7710	−	32.5123i	0.840306	−	1.45545i	0.889636	−	0.456670i	$-0.150958\pi$
$500$	−1.00000			−0.0447214
$501$	−23.2195	+	21.9399i	−1.03737	+	0.980205i
$502$	−0.0471320			−0.00210360
$503$	3.61707			0.161277			0.0806385	−	0.996743i	$-0.474304\pi$
$503$	3.61707			0.161277			0.0806385	+	0.996743i	$0.474304\pi$
$504$	3.39368	+	7.17516i	0.151167	+	0.319607i
$505$	−15.5695			−0.692835
$506$	−7.62440			−0.338946
$507$	−10.4142	−	3.10915i	−0.462511	−	0.138082i
$508$	4.92903			0.218691
$509$	7.78377	−	13.4819i	0.345010	−	0.597574i	−0.640346	−	0.768087i	$-0.721209\pi$
$509$	7.78377	−	13.4819i	0.345010	−	0.597574i	0.985356	+	0.170512i	$0.0545423\pi$
$510$	6.18718	−	5.84624i	0.273973	−	0.258876i
$511$	−21.1834	−	12.9513i	−0.937100	−	0.572931i
$512$	1.00000			0.0441942
$513$	6.97699	−	19.3066i	0.308042	−	0.852406i
$514$	−0.867267	+	1.50215i	−0.0382535	+	0.0662570i
$515$	8.60051	+	14.8965i	0.378984	+	0.656419i
$516$	16.2696	+	4.85728i	0.716231	+	0.213830i
$517$	−26.2682	−	45.4979i	−1.15528	−	2.00100i
$518$	11.1966	−	6.09420i	0.491953	−	0.267764i
$519$	−7.55934	−	31.7872i	−0.331818	−	1.39531i
$520$	4.39032			0.192528
$521$	−5.33460	+	9.23980i	−0.233713	+	0.404803i	−0.958898	−	0.283751i	$-0.908421\pi$
$521$	−5.33460	+	9.23980i	−0.233713	+	0.404803i	0.725185	+	0.688554i	$0.241754\pi$
$522$	−0.950364	+	16.7578i	−0.0415963	+	0.733467i
$523$	−13.2252	−	22.9067i	−0.578298	−	1.00164i	−0.995675	−	0.0929081i	$-0.970384\pi$
$523$	−13.2252	−	22.9067i	−0.578298	−	1.00164i	0.417377	−	0.908734i	$-0.362950\pi$
$524$	6.71245	−	11.6263i	0.293235	−	0.507898i
$525$	−3.06254	−	3.40894i	−0.133660	−	0.148778i
$526$	−6.53435	−	11.3178i	−0.284911	−	0.493480i
$527$	−8.69364	+	15.0578i	−0.378701	+	0.655929i
$528$	−5.40249	+	5.10479i	−0.235113	+	0.222157i
$529$	9.92165	+	17.1848i	0.431376	+	0.747165i
$530$	4.18972	+	7.25681i	0.181990	+	0.315216i
$531$	29.6666	−	14.9559i	1.28742	−	0.649030i
$532$	9.18082	−	4.99701i	0.398039	−	0.216648i
$533$	10.0566	−	17.4186i	0.435602	−	0.754484i
$534$	16.4862	−	15.5777i	0.713428	−	0.674115i
$535$	13.3307			0.576336
$536$	9.14081			0.394823
$537$	−22.5476	−	6.73156i	−0.973000	−	0.290488i
$538$	−10.0426	+	17.3942i	−0.432965	+	0.749918i
$539$	−13.6925	−	26.7369i	−0.589778	−	1.15164i
$540$	−5.11513	+	0.914017i	−0.220120	+	0.0393330i
$541$	−12.3933	−	21.4658i	−0.532829	−	0.922886i	−0.999265	−	0.0383315i	$-0.987796\pi$
$541$	−12.3933	−	21.4658i	−0.532829	−	0.922886i	0.466436	−	0.884555i	$-0.345538\pi$
$542$	−3.48267	−	6.03216i	−0.149593	−	0.259103i
$543$	−8.98298	−	37.7737i	−0.385497	−	1.62102i
$544$	2.45730	−	4.25616i	0.105356	−	0.182481i
$545$	−1.19326	−	2.06678i	−0.0511135	−	0.0885311i
$546$	13.4455	+	14.9663i	0.575414	+	0.640500i
$547$	−20.1416	+	34.8862i	−0.861191	+	1.49163i	0.00958910	+	0.999954i	$0.496948\pi$
$547$	−20.1416	+	34.8862i	−0.861191	+	1.49163i	−0.870780	+	0.491673i	$0.836386\pi$
$548$	−5.91661	−	10.2479i	−0.252745	−	0.437767i
$549$	14.6759	−	7.39859i	0.626353	−	0.315764i
$550$	2.14565	−	3.71637i	0.0914908	−	0.158467i
$551$	22.1039			0.941657
$552$	−2.94875	−	0.880345i	−0.125507	−	0.0374700i
$553$	−0.0733411	+	2.91538i	−0.00311878	+	0.123974i
$554$	6.55182	+	11.3481i	0.278360	+	0.482134i
$555$	1.93076	+	8.11892i	0.0819564	+	0.344629i
$556$	1.90549	+	3.30041i	0.0808109	+	0.139969i
$557$	17.3067	−	29.9762i	0.733310	−	1.27013i	−0.222151	−	0.975012i	$-0.571308\pi$
$557$	17.3067	−	29.9762i	0.733310	−	1.27013i	0.955461	−	0.295118i	$-0.0953590\pi$
$558$	9.47743	−	4.77787i	0.401212	−	0.202264i
$559$	43.0381			1.82032
$560$	−2.25729	−	1.38008i	−0.0953881	−	0.0583190i
$561$	8.45128	+	35.5379i	0.356813	+	1.50041i
$562$	10.0445	−	17.3975i	0.423700	−	0.733870i
$563$	26.7811			1.12869			0.564345	−	0.825539i	$-0.309129\pi$
$563$	26.7811			1.12869			0.564345	+	0.825539i	$0.309129\pi$
$564$	−4.90589	−	20.6294i	−0.206575	−	0.868655i
$565$	−6.21948			−0.261656
$566$	7.90498			0.332271
$567$	−18.7811	−	14.6380i	−0.788732	−	0.614737i
$568$	−4.03887			−0.169467
$569$	10.1983			0.427534			0.213767	−	0.976885i	$-0.431427\pi$
$569$	10.1983			0.427534			0.213767	+	0.976885i	$0.431427\pi$
$570$	1.58315	+	6.65720i	0.0663110	+	0.278839i
$571$	17.7581			0.743155			0.371578	−	0.928402i	$-0.378817\pi$
$571$	17.7581			0.743155			0.371578	+	0.928402i	$0.378817\pi$
$572$	−9.42008	+	16.3161i	−0.393873	+	0.682209i
$573$	2.81598	+	11.8413i	0.117639	+	0.494677i
$574$	−10.6461	+	5.79457i	−0.444361	+	0.241861i
$575$	1.77671			0.0740940
$576$	−2.67884	+	1.35049i	−0.111618	+	0.0562703i
$577$	−0.572592	+	0.991758i	−0.0238373	+	0.0412874i	−0.877698	−	0.479214i	$-0.840922\pi$
$577$	−0.572592	+	0.991758i	−0.0238373	+	0.0412874i	0.853861	+	0.520502i	$0.174255\pi$
$578$	−3.57661	−	6.19488i	−0.148768	−	0.257673i
$579$	1.31632	+	5.53518i	0.0547046	+	0.230034i
$580$	−2.79745	−	4.84532i	−0.116158	−	0.201191i
$581$	−15.0593	−	9.20706i	−0.624765	−	0.381973i
$582$	2.93336	+	0.875753i	0.121592	+	0.0363011i
$583$	−35.9587			−1.48926
$584$	4.69222	−	8.12716i	0.194165	−	0.336304i
$585$	−11.7610	+	5.92907i	−0.486256	+	0.245137i
$586$	14.8537	+	25.7273i	0.613599	+	1.06279i
$587$	−3.68073	+	6.37521i	−0.151920	+	0.263133i	−0.931933	−	0.362630i	$-0.881879\pi$
$587$	−3.68073	+	6.37521i	−0.151920	+	0.263133i	0.780013	+	0.625763i	$0.215212\pi$
$588$	−2.20843	−	11.9215i	−0.0910743	−	0.491636i
$589$	−6.98861	−	12.1046i	−0.287961	−	0.498762i
$590$	−5.53721	+	9.59074i	−0.227963	+	0.394844i
$591$	1.38042	+	5.80472i	0.0567831	+	0.238774i
$592$	2.40909	+	4.17267i	0.0990131	+	0.171496i
$593$	−1.79731	−	3.11303i	−0.0738067	−	0.127837i	0.826760	−	0.562555i	$-0.190181\pi$
$593$	−1.79731	−	3.11303i	−0.0738067	−	0.127837i	−0.900567	+	0.434718i	$0.856848\pi$
$594$	7.57845	−	20.9709i	0.310948	−	0.860447i
$595$	−11.4207	+	6.21615i	−0.468203	+	0.254837i
$596$	−4.50969	+	7.81101i	−0.184724	+	0.319951i
$597$	−29.6018	−	8.83760i	−1.21152	−	0.361699i
$598$	−7.80032			−0.318979
$599$	−26.9198			−1.09991			−0.549956	−	0.835193i	$-0.685356\pi$
$599$	−26.9198			−1.09991			−0.549956	+	0.835193i	$0.685356\pi$
$600$	1.25894	−	1.18957i	0.0513960	−	0.0485639i
$601$	−6.07464	+	10.5216i	−0.247790	+	0.429184i	−0.962912	−	0.269815i	$-0.913038\pi$
$601$	−6.07464	+	10.5216i	−0.247790	+	0.429184i	0.715123	+	0.698999i	$0.246371\pi$
$602$	−22.1282	−	13.5289i	−0.901877	−	0.551396i
$603$	−24.4868	+	12.3446i	−0.997178	+	0.502709i
$604$	6.92316	+	11.9913i	0.281700	+	0.487918i
$605$	3.70763	+	6.42180i	0.150737	+	0.261083i
$606$	19.6011	−	18.5210i	0.796240	−	0.752364i
$607$	21.5796	−	37.3770i	0.875891	−	1.51709i	0.0200797	−	0.999798i	$-0.493608\pi$
$607$	21.5796	−	37.3770i	0.875891	−	1.51709i	0.855811	−	0.517289i	$-0.173059\pi$
$608$	1.97536	+	3.42143i	0.0801115	+	0.138757i
$609$	7.95013	−	24.3753i	0.322156	−	0.987737i
$610$	−2.73923	+	4.74448i	−0.110908	+	0.192099i
$611$	−26.8744	−	46.5478i	−1.08722	−	1.88312i
$612$	−0.834806	+	14.7201i	−0.0337450	+	0.595026i
$613$	6.53756	−	11.3234i	0.264049	−	0.457347i	−0.703265	−	0.710928i	$-0.748275\pi$
$613$	6.53756	−	11.3234i	0.264049	−	0.457347i	0.967314	+	0.253581i	$0.0816085\pi$
$614$	−12.9068			−0.520876
$615$	−1.83583	−	7.71973i	−0.0740279	−	0.311290i
$616$	9.97226	−	5.42778i	0.401794	−	0.218692i
$617$	10.2243	+	17.7090i	0.411615	+	0.712938i	0.995067	−	0.0992101i	$-0.0316316\pi$
$617$	10.2243	+	17.7090i	0.411615	+	0.712938i	−0.583452	+	0.812148i	$0.698298\pi$
$618$	−28.5479	−	8.52295i	−1.14837	−	0.342843i
$619$	−11.6601	−	20.1958i	−0.468658	−	0.811739i	0.530700	−	0.847559i	$-0.321929\pi$
$619$	−11.6601	−	20.1958i	−0.468658	−	0.811739i	−0.999358	+	0.0358203i	$0.988596\pi$
$620$	−1.76894	+	3.06390i	−0.0710425	+	0.123049i
$621$	9.08811	−	1.62394i	0.364693	−	0.0651666i
$622$	17.5015			0.701745
$623$	−30.4313	+	16.5634i	−1.21920	+	0.663598i
$624$	−5.52715	+	5.22257i	−0.221263	+	0.209070i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	32.8823			1.31424
$627$	−28.1375	−	8.40043i	−1.12370	−	0.335481i
$628$	21.0517			0.840055
$629$	23.6794			0.944160
$630$	7.91071	+	0.648564i	0.315170	+	0.0258394i
$631$	−8.68367			−0.345691			−0.172846	−	0.984949i	$-0.555296\pi$
$631$	−8.68367			−0.345691			−0.172846	+	0.984949i	$0.555296\pi$
$632$	−1.10226			−0.0438454
$633$	−23.9711	+	22.6502i	−0.952767	+	0.900265i
$634$	4.00696			0.159137
$635$	2.46452	−	4.26867i	0.0978014	−	0.169397i
$636$	−13.9071	−	4.15194i	−0.551451	−	0.164635i
$637$	−14.0084	−	27.3538i	−0.555034	−	1.08380i
$638$	24.0094			0.950540
$639$	10.8195	−	5.45444i	0.428012	−	0.215774i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	0.603278	+	1.04491i	0.0238280	+	0.0412714i	0.877694	−	0.479222i	$-0.159081\pi$
$641$	0.603278	+	1.04491i	0.0238280	+	0.0412714i	−0.853865	+	0.520494i	$0.825748\pi$
$642$	−16.7826	+	15.8578i	−0.662355	+	0.625856i
$643$	14.1197	+	24.4560i	0.556825	+	0.964449i	0.997759	+	0.0669097i	$0.0213140\pi$
$643$	14.1197	+	24.4560i	0.556825	+	0.964449i	−0.440934	+	0.897540i	$0.645353\pi$
$644$	4.01056	+	2.45200i	0.158038	+	0.0966225i
$645$	12.3414	−	11.6613i	0.485940	−	0.459162i
$646$	19.4162			0.763920
$647$	−19.4036	+	33.6081i	−0.762836	+	1.32127i	0.178547	+	0.983931i	$0.442860\pi$
$647$	−19.4036	+	33.6081i	−0.762836	+	1.32127i	−0.941383	+	0.337339i	$0.890473\pi$
$648$	5.35236	−	7.23548i	0.210261	−	0.284237i
$649$	−23.7618	−	41.1567i	−0.932734	−	1.61554i
$650$	2.19516	−	3.80213i	0.0861012	−	0.149132i
$651$	−15.8621	+	3.35308i	−0.621685	+	0.131418i
$652$	2.03798	+	3.52989i	0.0798135	+	0.138241i
$653$	10.1874	−	17.6451i	0.398663	−	0.690505i	−0.594898	−	0.803801i	$-0.702808\pi$
$653$	10.1874	−	17.6451i	0.398663	−	0.690505i	0.993561	+	0.113296i	$0.0361409\pi$
$654$	3.96081	+	1.18250i	0.154880	+	0.0462392i
$655$	−6.71245	−	11.6263i	−0.262277	−	0.454278i
$656$	−2.29064	−	3.96751i	−0.0894346	−	0.154905i
$657$	−1.59407	+	28.1082i	−0.0621904	+	1.09660i
$658$	−0.814586	+	32.3805i	−0.0317559	+	1.26232i
$659$	−19.8911	+	34.4524i	−0.774848	+	1.34208i	0.160032	+	0.987112i	$0.448840\pi$
$659$	−19.8911	+	34.4524i	−0.774848	+	1.34208i	−0.934880	+	0.354964i	$0.884493\pi$
$660$	1.71963	+	7.23109i	0.0669365	+	0.281470i
$661$	−15.7090			−0.611011			−0.305506	−	0.952190i	$-0.598825\pi$
$661$	−15.7090			−0.611011			−0.305506	+	0.952190i	$0.598825\pi$
$662$	−35.3089			−1.37232
$663$	8.64628	+	36.3579i	0.335794	+	1.41202i
$664$	3.33570	−	5.77760i	0.129450	−	0.224214i
$665$	0.262870	−	10.4493i	0.0101937	−	0.405208i
$666$	−12.0887	−	7.92446i	−0.468428	−	0.307067i
$667$	4.97026	+	8.60874i	0.192449	+	0.333332i
$668$	9.22182	+	15.9727i	0.356803	+	0.618001i
$669$	32.4318	+	9.68247i	1.25389	+	0.374346i
$670$	4.57040	−	7.91617i	0.176570	−	0.305828i
$671$	−11.7549	−	20.3600i	−0.453791	−	0.785989i
$672$	4.48350	−	0.947763i	0.172955	−	0.0365608i
$673$	9.82133	−	17.0110i	0.378584	−	0.655728i	−0.612272	−	0.790647i	$-0.709744\pi$
$673$	9.82133	−	17.0110i	0.378584	−	0.655728i	0.990857	+	0.134920i	$0.0430776\pi$
$674$	−14.0339	−	24.3074i	−0.540565	−	0.936285i
$675$	−1.76600	+	4.88684i	−0.0679735	+	0.188095i
$676$	−3.13744	+	5.43421i	−0.120671	+	0.209008i
$677$	0.251707			0.00967388			0.00483694	−	0.999988i	$-0.498460\pi$
$677$	0.251707			0.00967388			0.00483694	+	0.999988i	$0.498460\pi$
$678$	7.82996	−	7.39849i	0.300708	−	0.284137i
$679$	−3.98964	−	2.43921i	−0.153108	−	0.0936084i
$680$	−2.45730	−	4.25616i	−0.0942330	−	0.163216i
$681$	−6.28659	+	5.94016i	−0.240903	+	0.227628i
$682$	−7.59107	−	13.1481i	−0.290677	−	0.503467i
$683$	−14.7651	+	25.5739i	−0.564971	+	0.978559i	0.432081	+	0.901835i	$0.357779\pi$
$683$	−14.7651	+	25.5739i	−0.564971	+	0.978559i	−0.997052	+	0.0767243i	$0.975554\pi$
$684$	−9.91227	−	6.49775i	−0.379005	−	0.248448i
$685$	−11.8332			−0.452124
$686$	−1.39610	+	18.4676i	−0.0533035	+	0.705095i
$687$	−7.49934	−	2.23892i	−0.286118	−	0.0854201i
$688$	4.90148	−	8.48962i	0.186867	−	0.323664i
$689$	−36.7884			−1.40153
$690$	−2.23677	+	2.11352i	−0.0851525	+	0.0804602i
$691$	9.80626			0.373048			0.186524	−	0.982450i	$-0.440278\pi$
$691$	9.80626			0.373048			0.186524	+	0.982450i	$0.440278\pi$
$692$	−18.8642			−0.717109
$693$	−19.3839	+	28.0076i	−0.736334	+	1.06392i
$694$	17.6505			0.670003
$695$	3.81099			0.144559
$696$	9.28565	+	2.77222i	0.351972	+	0.105081i
$697$	−22.5152			−0.852822
$698$	7.74918	−	13.4220i	0.293311	−	0.508029i
$699$	27.2770	−	25.7739i	1.03171	−	0.974859i
$700$	−2.32383	+	1.26483i	−0.0878326	+	0.0478062i
$701$	9.89302			0.373654			0.186827	−	0.982393i	$-0.440180\pi$
$701$	9.89302			0.373654			0.186827	+	0.982393i	$0.440180\pi$
$702$	7.75332	−	21.4548i	0.292630	−	0.809759i
$703$	−9.51766	+	16.4851i	−0.358965	+	0.621746i
$704$	2.14565	+	3.71637i	0.0808672	+	0.140066i
$705$	−20.3185	−	6.06608i	−0.765241	−	0.228462i
$706$	−4.88224	−	8.45629i	−0.183746	−	0.318257i
$707$	−36.1810	+	19.6929i	−1.36072	+	0.740627i
$708$	−4.43780	−	18.6611i	−0.166783	−	0.701325i
$709$	10.6044			0.398257			0.199128	−	0.979973i	$-0.436189\pi$
$709$	10.6044			0.398257			0.199128	+	0.979973i	$0.436189\pi$
$710$	−2.01943	+	3.49776i	−0.0757880	+	0.131269i
$711$	2.95277	−	1.48859i	0.110738	−	0.0558263i
$712$	−6.54765	−	11.3409i	−0.245384	−	0.425017i
$713$	3.14290	−	5.44366i	0.117703	−	0.203867i
$714$	6.98345	−	21.4114i	0.261349	−	0.801303i
$715$	9.42008	+	16.3161i	0.352291	+	0.610186i
$716$	−6.79281	+	11.7655i	−0.253859	+	0.439697i
$717$	18.1543	−	17.1539i	0.677984	−	0.640623i
$718$	8.43793	+	14.6149i	0.314901	+	0.545424i
$719$	−14.6773	−	25.4219i	−0.547371	−	0.948075i	−0.998454	−	0.0555927i	$-0.982295\pi$
$719$	−14.6773	−	25.4219i	−0.547371	−	0.948075i	0.451082	−	0.892482i	$-0.351038\pi$
$720$	−0.169863	+	2.99519i	−0.00633041	+	0.111624i
$721$	38.8278	+	23.7388i	1.44602	+	0.884078i
$722$	1.69589	−	2.93737i	0.0631145	−	0.109318i
$723$	7.65600	−	7.23412i	0.284730	−	0.269040i
$724$	−22.4169			−0.833116
$725$	−5.59489			−0.207789
$726$	−12.3068	−	3.67419i	−0.456750	−	0.136362i
$727$	13.7335	−	23.7871i	0.509346	−	0.882213i	−0.490596	−	0.871387i	$-0.663221\pi$
$727$	13.7335	−	23.7871i	0.509346	−	0.882213i	0.999941	−	0.0108255i	$-0.00344594\pi$
$728$	10.2024	−	5.55302i	0.378125	−	0.205809i
$729$	−4.56669	+	26.6110i	−0.169137	+	0.985593i
$730$	−4.69222	−	8.12716i	−0.173667	−	0.300800i
$731$	−24.0888	−	41.7230i	−0.890956	−	1.54318i
$732$	−2.19535	−	9.23152i	−0.0811426	−	0.341207i
$733$	12.6470	−	21.9053i	0.467129	−	0.809090i	−0.532166	−	0.846640i	$-0.678622\pi$
$733$	12.6470	−	21.9053i	0.467129	−	0.809090i	0.999295	+	0.0375496i	$0.0119552\pi$
$734$	3.80501	+	6.59048i	0.140446	+	0.243259i
$735$	−11.4286	−	4.04820i	−0.421549	−	0.149320i
$736$	−0.888355	+	1.53868i	−0.0327452	+	0.0567164i
$737$	19.6130	+	33.9707i	0.722453	+	1.25133i
$738$	11.4943	+	7.53483i	0.423112	+	0.277361i
$739$	−3.71100	+	6.42765i	−0.136511	+	0.236445i	−0.926174	−	0.377097i	$-0.876922\pi$
$739$	−3.71100	+	6.42765i	−0.136511	+	0.236445i	0.789662	+	0.613542i	$0.210256\pi$
$740$	4.81818			0.177120
$741$	−28.7868	−	8.59426i	−1.05751	−	0.315718i
$742$	18.9149	+	11.5643i	0.694387	+	0.424539i
$743$	−23.1847	−	40.1571i	−0.850564	−	1.47322i	−0.880700	−	0.473674i	$-0.842927\pi$
$743$	−23.1847	−	40.1571i	−0.850564	−	1.47322i	0.0301361	−	0.999546i	$-0.490406\pi$
$744$	−1.41772	−	5.96154i	−0.0519761	−	0.218561i
$745$	4.50969	+	7.81101i	0.165222	+	0.286173i
$746$	5.46643	−	9.46813i	0.200140	−	0.346653i
$747$	−1.13322	+	19.9821i	−0.0414624	+	0.731106i
$748$	21.0900			0.771127
$749$	30.9783	−	16.8611i	1.13192	−	0.616092i
$750$	−0.400725	−	1.68506i	−0.0146324	−	0.0615296i
$751$	14.9868	−	25.9579i	0.546875	−	0.947216i	−0.451611	−	0.892215i	$-0.649150\pi$
$751$	14.9868	−	25.9579i	0.546875	−	0.947216i	0.998486	−	0.0550009i	$-0.0175162\pi$
$752$	−12.2426			−0.446440
$753$	−0.0188870	−	0.0794202i	−0.000688279	−	0.00289423i
$754$	24.5634			0.894545
$755$	13.8463			0.503920
$756$	−10.7306	+	8.59382i	−0.390269	+	0.312554i
$757$	0.221986			0.00806821			0.00403410	−	0.999992i	$-0.498716\pi$
$757$	0.221986			0.00806821			0.00403410	+	0.999992i	$0.498716\pi$
$758$	−15.9380			−0.578893
$759$	−3.05528	−	12.8476i	−0.110900	−	0.466337i
$760$	3.95072			0.143308
$761$	24.5283	−	42.4842i	0.889150	−	1.54005i	0.0482677	−	0.998834i	$-0.484630\pi$
$761$	24.5283	−	42.4842i	0.889150	−	1.54005i	0.840882	−	0.541218i	$-0.182037\pi$
$762$	1.97519	+	8.30571i	0.0715534	+	0.300884i
$763$	−5.38706	−	3.29358i	−0.195025	−	0.119236i
$764$	7.02722			0.254236
$765$	12.3306	+	8.08303i	0.445814	+	0.292242i
$766$	3.36190	−	5.82298i	0.121470	−	0.210393i
$767$	−24.3101	−	42.1064i	−0.877788	−	1.52037i
$768$	0.400725	+	1.68506i	0.0144599	+	0.0608043i
$769$	23.5625	+	40.8114i	0.849684	+	1.47170i	0.881490	+	0.472202i	$0.156541\pi$
$769$	23.5625	+	40.8114i	0.849684	+	1.47170i	−0.0318059	+	0.999494i	$0.510126\pi$
$770$	0.285531	−	11.3501i	0.0102898	−	0.409030i
$771$	−2.87875	−	0.859447i	−0.103676	−	0.0309522i
$772$	3.28486			0.118225
$773$	5.72363	−	9.91361i	0.205865	−	0.356568i	−0.744543	−	0.667574i	$-0.767333\pi$
$773$	5.72363	−	9.91361i	0.205865	−	0.356568i	0.950408	+	0.311006i	$0.100666\pi$
$774$	−1.66516	+	29.3617i	−0.0598529	+	1.05539i
$775$	1.76894	+	3.06390i	0.0635423	+	0.110059i
$776$	0.883722	−	1.53065i	0.0317238	−	0.0549472i
$777$	14.7559	+	16.4249i	0.529364	+	0.589240i
$778$	4.52819	+	7.84305i	0.162343	+	0.281187i
$779$	9.04969	−	15.6745i	0.324239	−	0.561598i
$780$	1.75931	+	7.39794i	0.0629933	+	0.264889i
$781$	−8.66599	−	15.0099i	−0.310094	−	0.537098i
$782$	4.36591	+	7.56197i	0.156124	+	0.270416i
$783$	−28.6186	+	5.11383i	−1.02275	+	0.182753i
$784$	−6.99115	−	0.351971i	−0.249684	−	0.0125704i
$785$	10.5259	−	18.2313i	0.375684	−	0.650704i
$786$	22.2809	+	6.65192i	0.794732	+	0.237266i
$787$	−48.4542			−1.72721			−0.863603	−	0.504172i	$-0.831798\pi$
$787$	−48.4542			−1.72721			−0.863603	+	0.504172i	$0.831798\pi$
$788$	3.44482			0.122717
$789$	16.4527	−	15.5461i	0.585732	−	0.553455i
$790$	−0.551129	+	0.954583i	−0.0196083	+	0.0339625i
$791$	−14.4530	+	7.86661i	−0.513890	+	0.279705i
$792$	−10.7668	−	7.05790i	−0.382581	−	0.250791i
$793$	−12.0261	−	20.8298i	−0.427059	−	0.739688i
$794$	16.9811	+	29.4122i	0.602638	+	1.04380i
$795$	−10.5492	+	9.96790i	−0.374142	+	0.353525i
$796$	−8.91802	+	15.4465i	−0.316091	+	0.547485i
$797$	−3.67348	−	6.36265i	−0.130121	−	0.225377i	0.793602	−	0.608437i	$-0.208203\pi$
$797$	−3.67348	−	6.36265i	−0.130121	−	0.225377i	−0.923723	+	0.383061i	$0.874870\pi$
$798$	12.0992	+	13.4678i	0.428308	+	0.476754i
$799$	−30.0836	+	52.1063i	−1.06428	+	1.84339i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	32.8558	+	21.5378i	1.16090	+	0.761002i
$802$	−15.3883	+	26.6533i	−0.543379	+	0.941160i
$803$	40.2714			1.42115
$804$	3.66295	+	15.4028i	0.129182	+	0.543214i
$805$	4.12878	−	2.24724i	0.145520	−	0.0792050i
$806$	−7.76622	−	13.4515i	−0.273554	−	0.473809i
$807$	−33.3346	−	9.95200i	−1.17343	−	0.350327i
$808$	−7.78476	−	13.4836i	−0.273867	−	0.474352i
$809$	3.07454	−	5.32525i	0.108095	−	0.187226i	−0.806904	−	0.590683i	$-0.798858\pi$
$809$	3.07454	−	5.32525i	0.108095	−	0.187226i	0.914998	+	0.403457i	$0.132192\pi$
$810$	−3.58993	−	8.25302i	−0.126137	−	0.289982i
$811$	14.7407			0.517617			0.258809	−	0.965929i	$-0.416670\pi$
$811$	14.7407			0.517617			0.258809	+	0.965929i	$0.416670\pi$
$812$	−12.6293	−	7.72140i	−0.443202	−	0.270968i
$813$	8.76894	−	8.28573i	0.307540	−	0.290593i
$814$	−10.3381	+	17.9062i	−0.362352	+	0.627611i
$815$	4.07596			0.142775
$816$	8.15658	+	2.43514i	0.285537	+	0.0852469i
$817$	38.7288			1.35495
$818$	−12.7154			−0.444585
$819$	−19.8312	+	28.6538i	−0.692958	+	1.00125i
$820$	−4.58128			−0.159985
$821$	42.7070			1.49049			0.745243	−	0.666793i	$-0.232333\pi$
$821$	42.7070			1.49049			0.745243	+	0.666793i	$0.232333\pi$
$822$	14.8973	−	14.0764i	0.519604	−	0.490971i
$823$	49.5468			1.72709			0.863546	−	0.504270i	$-0.168239\pi$
$823$	49.5468			1.72709			0.863546	+	0.504270i	$0.168239\pi$
$824$	−8.60051	+	14.8965i	−0.299613	+	0.518945i
$825$	7.12212	+	2.12630i	0.247960	+	0.0740283i
$826$	−0.736862	+	29.2909i	−0.0256387	+	1.01916i
$827$	−19.1520			−0.665979			−0.332990	−	0.942930i	$-0.608057\pi$
$827$	−19.1520			−0.665979			−0.332990	+	0.942930i	$0.608057\pi$
$828$	0.301797	−	5.32158i	0.0104882	−	0.184938i
$829$	10.7884	−	18.6860i	0.374696	−	0.648993i	−0.615585	−	0.788070i	$-0.711080\pi$
$829$	10.7884	−	18.6860i	0.374696	−	0.648993i	0.990282	+	0.139077i	$0.0444136\pi$
$830$	−3.33570	−	5.77760i	−0.115784	−	0.200543i
$831$	−16.4967	+	15.5876i	−0.572264	+	0.540730i
$832$	2.19516	+	3.80213i	0.0761034	+	0.131815i
$833$	−18.6774	+	28.8906i	−0.647132	+	1.00100i
$834$	−4.79781	+	4.53342i	−0.166134	+	0.156980i
$835$	18.4436			0.638269
$836$	−8.47687	+	14.6824i	−0.293179	+	0.507800i
$837$	11.8488	+	14.0554i	0.409556	+	0.485826i
$838$	4.84388	+	8.38985i	0.167329	+	0.289823i
$839$	15.4373	−	26.7382i	0.532955	−	0.923106i	−0.466304	−	0.884625i	$-0.654415\pi$
$839$	15.4373	−	26.7382i	0.532955	−	0.923106i	0.999259	−	0.0384813i	$-0.0122520\pi$
$840$	1.42096	−	4.35670i	0.0490278	−	0.150321i
$841$	−1.15142	−	1.99433i	−0.0397043	−	0.0687699i
$842$	−14.3536	+	24.8611i	−0.494657	+	0.856771i
$843$	33.3409	+	9.95388i	1.14832	+	0.342830i
$844$	9.52036	+	16.4897i	0.327704	+	0.567600i
$845$	3.13744	+	5.43421i	0.107931	+	0.186942i
$846$	32.7959	−	16.5334i	1.12754	−	0.568431i
$847$	16.7384	+	10.2336i	0.575139	+	0.351632i
$848$	−4.18972	+	7.25681i	−0.143876	+	0.249200i
$849$	3.16772	+	13.3203i	0.108716	+	0.457153i
$850$	−4.91459			−0.168569
$851$	−8.56052			−0.293451
$852$	−1.61847	−	6.80572i	−0.0554480	−	0.233160i
$853$	−8.25999	+	14.3067i	−0.282817	+	0.489853i	−0.972077	−	0.234660i	$-0.924602\pi$
$853$	−8.25999	+	14.3067i	−0.282817	+	0.489853i	0.689261	+	0.724514i	$0.257936\pi$
$854$	−0.364522	+	14.4901i	−0.0124737	+	0.495839i
$855$	−10.5834	+	5.33541i	−0.361943	+	0.182467i
$856$	6.66535	+	11.5447i	0.227817	+	0.394591i
$857$	13.7932	+	23.8906i	0.471168	+	0.816086i	0.999456	−	0.0329787i	$-0.0104994\pi$
$857$	13.7932	+	23.8906i	0.471168	+	0.816086i	−0.528288	+	0.849065i	$0.677166\pi$
$858$	−31.2684	−	9.33514i	−1.06748	−	0.318696i
$859$	−5.04949	+	8.74597i	−0.172286	+	0.298409i	−0.939219	−	0.343319i	$-0.888449\pi$
$859$	−5.04949	+	8.74597i	−0.172286	+	0.298409i	0.766933	+	0.641728i	$0.221782\pi$
$860$	−4.90148	−	8.48962i	−0.167139	−	0.289494i
$861$	−14.0303	−	15.6173i	−0.478153	−	0.532237i
$862$	3.62516	−	6.27897i	0.123474	−	0.213862i
$863$	18.4442	+	31.9462i	0.627847	+	1.08746i	0.987983	+	0.154563i	$0.0493970\pi$
$863$	18.4442	+	31.9462i	0.627847	+	1.08746i	−0.360136	+	0.932900i	$0.617270\pi$
$864$	−3.34913	−	3.97283i	−0.113940	−	0.135158i
$865$	−9.43209	+	16.3369i	−0.320701	+	0.555470i
$866$	−18.8871			−0.641808
$867$	9.00549	−	8.50924i	0.305842	−	0.288989i
$868$	−0.235401	+	9.35741i	−0.00799004	+	0.317611i
$869$	−2.36506	−	4.09640i	−0.0802291	−	0.138961i
$870$	7.04364	−	6.65550i	0.238802	−	0.225643i
$871$	20.0655	+	34.7545i	0.679894	+	1.17761i
$872$	1.19326	−	2.06678i	0.0404087	−	0.0699900i
$873$	−0.300223	+	5.29382i	−0.0101610	+	0.179169i
$874$	−7.01929			−0.237431
$875$	−0.0665372	+	2.64491i	−0.00224937	+	0.0894144i
$876$	15.5750	+	4.64991i	0.526231	+	0.157106i
$877$	−29.2698	+	50.6968i	−0.988371	+	1.71191i	−0.362498	+	0.931984i	$0.618076\pi$
$877$	−29.2698	+	50.6968i	−0.988371	+	1.71191i	−0.625873	+	0.779925i	$0.715257\pi$
$878$	2.09125			0.0705764
$879$	−37.3998	+	35.3389i	−1.26146	+	1.19195i
$880$	4.29130			0.144660
$881$	37.8045			1.27367			0.636833	−	0.771002i	$-0.280244\pi$
$881$	37.8045			1.27367			0.636833	+	0.771002i	$0.280244\pi$
$882$	19.2035	−	8.49859i	0.646615	−	0.286162i
$883$	−26.8151			−0.902400			−0.451200	−	0.892423i	$-0.649004\pi$
$883$	−26.8151			−0.902400			−0.451200	+	0.892423i	$0.649004\pi$
$884$	21.5766			0.725700
$885$	−18.3798	−	5.48728i	−0.617832	−	0.184453i
$886$	−11.8707			−0.398803
$887$	10.0193	−	17.3540i	0.336416	−	0.582689i	−0.647340	−	0.762201i	$-0.724119\pi$
$887$	10.0193	−	17.3540i	0.336416	−	0.582689i	0.983756	+	0.179512i	$0.0574520\pi$
$888$	−6.06581	+	5.73155i	−0.203555	+	0.192338i
$889$	0.327964	−	13.0369i	0.0109996	−	0.437243i
$890$	−13.0953			−0.438956
$891$	38.3741	+	4.36657i	1.28558	+	0.146286i
$892$	9.77058	−	16.9231i	0.327143	−	0.566629i
$893$	−24.1835	−	41.8870i	−0.809269	−	1.40170i
$894$	−14.9691	−	4.46902i	−0.500643	−	0.149466i
$895$	6.79281	+	11.7655i	0.227059	+	0.393277i
$896$	0.0665372	−	2.64491i	0.00222285	−	0.0883604i
$897$	−3.12578	−	13.1440i	−0.104367	−	0.438865i
$898$	21.7279			0.725068
$899$	−9.89705	+	17.1422i	−0.330085	+	0.571724i
$900$	2.50898	+	1.64470i	0.0836326	+	0.0548233i
$901$	20.5908	+	35.6643i	0.685978	+	1.18815i
$902$	9.82983	−	17.0258i	0.327298	−	0.566896i
$903$	13.9296	−	42.7086i	0.463549	−	1.42125i
$904$	−3.10974	−	5.38623i	−0.103428	−	0.179143i
$905$	−11.2084	+	19.4136i	−0.372581	+	0.645329i
$906$	−17.4317	+	16.4711i	−0.579130	+	0.547217i
$907$	−28.2924	−	49.0038i	−0.939432	−	1.62714i	−0.766533	−	0.642205i	$-0.778020\pi$
$907$	−28.2924	−	49.0038i	−0.939432	−	1.62714i	−0.172899	−	0.984939i	$-0.555314\pi$
$908$	2.49678	+	4.32454i	0.0828584	+	0.143515i
$909$	39.0636	+	25.6072i	1.29566	+	0.849337i
$910$	0.292120	−	11.6120i	0.00968367	−	0.384934i
$911$	−6.29392	+	10.9014i	−0.208527	+	0.361179i	−0.951251	−	0.308419i	$-0.900200\pi$
$911$	−6.29392	+	10.9014i	−0.208527	+	0.361179i	0.742724	+	0.669598i	$0.233534\pi$
$912$	−4.97373	+	4.69965i	−0.164697	+	0.155621i
$913$	28.6290			0.947480
$914$	6.44326			0.213124
$915$	−9.09241	−	2.71453i	−0.300586	−	0.0897395i
$916$	−2.25929	+	3.91321i	−0.0746491	+	0.129296i
$917$	−30.3040	−	18.5275i	−1.00073	−	0.611830i
$918$	−25.1388	+	4.49202i	−0.829704	+	0.148259i
$919$	22.4277	+	38.8460i	0.739823	+	1.28141i	0.952575	+	0.304305i	$0.0984241\pi$
$919$	22.4277	+	38.8460i	0.739823	+	1.28141i	−0.212752	+	0.977106i	$0.568243\pi$
$920$	0.888355	+	1.53868i	0.0292882	+	0.0507287i
$921$	−5.17207	−	21.7487i	−0.170425	−	0.716644i
$922$	−0.496819	+	0.860516i	−0.0163619	+	0.0283396i
$923$	−8.86595	−	15.3563i	−0.291826	−	0.505458i
$924$	13.1423	+	14.6288i	0.432349	+	0.481252i
$925$	2.40909	−	4.17267i	0.0792105	−	0.137197i
$926$	8.98000	+	15.5538i	0.295101	+	0.511130i
$927$	2.92181	−	51.5203i	0.0959648	−	1.69215i
$928$	2.79745	−	4.84532i	0.0918307	−	0.159055i
$929$	−33.8185			−1.10955			−0.554775	−	0.832000i	$-0.687196\pi$
$929$	−33.8185			−1.10955			−0.554775	+	0.832000i	$0.687196\pi$
$930$	−5.87171	−	1.75299i	−0.192541	−	0.0574829i
$931$	−12.6058	−	24.6150i	−0.413138	−	0.806723i
$932$	−10.8333	−	18.7639i	−0.354857	−	0.614631i
$933$	7.01327	+	29.4910i	0.229604	+	0.965491i
$934$	0.111695	+	0.193461i	0.00365477	+	0.00633025i
$935$	10.5450	−	18.2645i	0.344858	−	0.597312i
$936$	−11.0152	−	7.22075i	−0.360043	−	0.236018i
$937$	4.01796			0.131261			0.0656304	−	0.997844i	$-0.479094\pi$
$937$	4.01796			0.131261			0.0656304	+	0.997844i	$0.479094\pi$
$938$	0.608204	−	24.1767i	0.0198586	−	0.789396i
$939$	13.1768	+	55.4086i	0.430007	+	1.80819i
$940$	−6.12128	+	10.6024i	−0.199654	+	0.345811i
$941$	−35.4422			−1.15538			−0.577691	−	0.816256i	$-0.696046\pi$
$941$	−35.4422			−1.15538			−0.577691	+	0.816256i	$0.696046\pi$
$942$	8.43594	+	35.4734i	0.274858	+	1.15578i
$943$	8.13962			0.265062
$944$	−11.0744			−0.360442
$945$	2.07715	+	13.5899i	0.0675697	+	0.442080i
$946$	42.0675			1.36773
$947$	27.5534			0.895365			0.447683	−	0.894193i	$-0.352249\pi$
$947$	27.5534			0.895365			0.447683	+	0.894193i	$0.352249\pi$
$948$	−0.441702	−	1.85737i	−0.0143458	−	0.0603245i
$949$	41.2007			1.33743
$950$	1.97536	−	3.42143i	0.0640892	−	0.111006i
$951$	1.60569	+	6.75195i	0.0520679	+	0.218947i
$952$	−11.0937	−	6.78253i	−0.359548	−	0.219823i
$953$	44.7444			1.44941			0.724706	−	0.689058i	$-0.241976\pi$
$953$	44.7444			1.44941			0.724706	+	0.689058i	$0.241976\pi$
$954$	1.42335	−	25.0980i	0.0460828	−	0.812578i
$955$	3.51361	−	6.08575i	0.113698	−	0.196930i
$956$	−7.21014	−	12.4883i	−0.233192	−	0.403901i
$957$	9.62115	+	40.4572i	0.311007	+	1.30779i
$958$	0.610293	+	1.05706i	0.0197177	+	0.0341520i
$959$	−27.4984	+	14.9671i	−0.887970	+	0.483312i
$960$	1.65967	+	0.495491i	0.0535655	+	0.0159919i
$961$	−18.4834			−0.596237
$962$	−10.5767	+	18.3193i	−0.341006	+	0.590639i
$963$	−33.4464	−	21.9250i	−1.07780	−	0.706523i
$964$	−3.04065	−	5.26656i	−0.0979328	−	0.169625i
$965$	1.64243	−	2.84477i	0.0528717	−	0.0915765i
$966$	−2.52464	+	7.74060i	−0.0812289	+	0.249050i
$967$	26.8486	+	46.5031i	0.863391	+	1.49544i	0.868636	+	0.495451i	$0.164997\pi$
$967$	26.8486	+	46.5031i	0.863391	+	1.49544i	−0.00524436	+	0.999986i	$0.501669\pi$
$968$	−3.70763	+	6.42180i	−0.119168	+	0.206404i
$969$	7.78055	+	32.7174i	0.249947	+	1.05104i
$970$	−0.883722	−	1.53065i	−0.0283746	−	0.0491462i
$971$	−15.6918	−	27.1791i	−0.503575	−	0.872217i	−0.999991	−	0.00413284i	$-0.998684\pi$
$971$	−15.6918	−	27.1791i	−0.503575	−	0.872217i	0.496417	−	0.868084i	$-0.334649\pi$
$972$	14.3370	+	6.11961i	0.459860	+	0.196286i
$973$	8.85609	−	4.82027i	0.283913	−	0.154531i
$974$	−19.6408	+	34.0188i	−0.629331	+	1.09003i
$975$	7.28646	+	2.17536i	0.233353	+	0.0696674i
$976$	−5.47846			−0.175361
$977$	36.4631			1.16656			0.583279	−	0.812272i	$-0.301769\pi$
$977$	36.4631			1.16656			0.583279	+	0.812272i	$0.301769\pi$
$978$	−5.13139	+	4.84863i	−0.164084	+	0.155042i
$979$	28.0979	−	48.6671i	0.898014	−	1.55541i
$980$	−3.80039	+	5.87852i	−0.121399	+	0.187783i
$981$	−0.405379	+	7.14805i	−0.0129428	+	0.228220i
$982$	4.41619	+	7.64907i	0.140926	+	0.244092i
$983$	7.43983	+	12.8862i	0.237294	+	0.411005i	0.959937	−	0.280217i	$-0.0904063\pi$
$983$	7.43983	+	12.8862i	0.237294	+	0.411005i	−0.722643	+	0.691221i	$0.757073\pi$
$984$	5.76756	−	5.44974i	0.183863	−	0.173731i
$985$	1.72241	−	2.98330i	0.0548806	−	0.0950559i
$986$	−13.7483	−	23.8128i	−0.437836	−	0.758354i
$987$	−54.8895	+	11.6030i	−1.74715	+	0.369329i
$988$	−8.67247	+	15.0212i	−0.275908	+	0.477886i
$989$	8.70852	+	15.0836i	0.276915	+	0.479630i
$990$	−11.4957	+	5.79535i	−0.365357	+	0.184188i
$991$	15.6408	−	27.0906i	0.496845	−	0.860561i	−0.503149	−	0.864200i	$-0.667825\pi$
$991$	15.6408	−	27.0906i	0.496845	−	0.860561i	0.999993	+	0.00363943i	$0.00115847\pi$
$992$	−3.53789			−0.112328
$993$	−14.1491	−	59.4975i	−0.449009	−	1.88810i
$994$	−0.268735	+	10.6825i	−0.00852375	+	0.338827i
$995$	8.91802	+	15.4465i	0.282720	+	0.489686i
$996$	11.0723	+	3.30562i	0.350839	+	0.104743i
$997$	20.0852	+	34.7886i	0.636105	+	1.10177i	0.986280	+	0.165082i	$0.0527887\pi$
$997$	20.0852	+	34.7886i	0.636105	+	1.10177i	−0.350175	+	0.936684i	$0.613878\pi$
$998$	18.7710	−	32.5123i	0.594186	−	1.02916i
$999$	8.50893	−	23.5457i	0.269211	−	0.744953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.h.151.4	yes	12
3.2	odd	2		1890.2.i.f.991.3		12
7.2	even	3		630.2.l.f.331.1	yes	12
9.4	even	3		630.2.l.f.571.1	yes	12
9.5	odd	6		1890.2.l.h.361.6		12
21.2	odd	6		1890.2.l.h.1801.6		12
63.23	odd	6		1890.2.i.f.1171.3		12
63.58	even	3	inner	630.2.i.h.121.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.h.121.4	✓	12	63.58	even	3	inner
630.2.i.h.151.4	yes	12	1.1	even	1	trivial
630.2.l.f.331.1	yes	12	7.2	even	3
630.2.l.f.571.1	yes	12	9.4	even	3
1890.2.i.f.991.3		12	3.2	odd	2
1890.2.i.f.1171.3		12	63.23	odd	6
1890.2.l.h.361.6		12	9.5	odd	6
1890.2.l.h.1801.6		12	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.400725 + 1.68506i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.400725 + 1.68506i) q^{6} +(0.0665372 - 2.64491i) q^{7} +1.00000 q^{8} +(-2.67884 + 1.35049i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.400725 + 1.68506i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.400725 + 1.68506i) q^{6} +(0.0665372 - 2.64491i) q^{7} +1.00000 q^{8} +(-2.67884 + 1.35049i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.14565 + 3.71637i) q^{11} +(0.400725 + 1.68506i) q^{12} +(2.19516 + 3.80213i) q^{13} +(0.0665372 - 2.64491i) q^{14} +(1.65967 + 0.495491i) q^{15} +1.00000 q^{16} +(2.45730 - 4.25616i) q^{17} +(-2.67884 + 1.35049i) q^{18} +(1.97536 + 3.42143i) q^{19} +(0.500000 - 0.866025i) q^{20} +(4.48350 - 0.947763i) q^{21} +(2.14565 + 3.71637i) q^{22} +(-0.888355 + 1.53868i) q^{23} +(0.400725 + 1.68506i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.19516 + 3.80213i) q^{26} +(-3.34913 - 3.97283i) q^{27} +(0.0665372 - 2.64491i) q^{28} +(2.79745 - 4.84532i) q^{29} +(1.65967 + 0.495491i) q^{30} -3.53789 q^{31} +1.00000 q^{32} +(-5.40249 + 5.10479i) q^{33} +(2.45730 - 4.25616i) q^{34} +(-2.25729 - 1.38008i) q^{35} +(-2.67884 + 1.35049i) q^{36} +(2.40909 + 4.17267i) q^{37} +(1.97536 + 3.42143i) q^{38} +(-5.52715 + 5.22257i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-2.29064 - 3.96751i) q^{41} +(4.48350 - 0.947763i) q^{42} +(4.90148 - 8.48962i) q^{43} +(2.14565 + 3.71637i) q^{44} +(-0.169863 + 2.99519i) q^{45} +(-0.888355 + 1.53868i) q^{46} -12.2426 q^{47} +(0.400725 + 1.68506i) q^{48} +(-6.99115 - 0.351971i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(8.15658 + 2.43514i) q^{51} +(2.19516 + 3.80213i) q^{52} +(-4.18972 + 7.25681i) q^{53} +(-3.34913 - 3.97283i) q^{54} +4.29130 q^{55} +(0.0665372 - 2.64491i) q^{56} +(-4.97373 + 4.69965i) q^{57} +(2.79745 - 4.84532i) q^{58} -11.0744 q^{59} +(1.65967 + 0.495491i) q^{60} -5.47846 q^{61} -3.53789 q^{62} +(3.39368 + 7.17516i) q^{63} +1.00000 q^{64} +4.39032 q^{65} +(-5.40249 + 5.10479i) q^{66} +9.14081 q^{67} +(2.45730 - 4.25616i) q^{68} +(-2.94875 - 0.880345i) q^{69} +(-2.25729 - 1.38008i) q^{70} -4.03887 q^{71} +(-2.67884 + 1.35049i) q^{72} +(4.69222 - 8.12716i) q^{73} +(2.40909 + 4.17267i) q^{74} +(1.25894 - 1.18957i) q^{75} +(1.97536 + 3.42143i) q^{76} +(9.97226 - 5.42778i) q^{77} +(-5.52715 + 5.22257i) q^{78} -1.10226 q^{79} +(0.500000 - 0.866025i) q^{80} +(5.35236 - 7.23548i) q^{81} +(-2.29064 - 3.96751i) q^{82} +(3.33570 - 5.77760i) q^{83} +(4.48350 - 0.947763i) q^{84} +(-2.45730 - 4.25616i) q^{85} +(4.90148 - 8.48962i) q^{86} +(9.28565 + 2.77222i) q^{87} +(2.14565 + 3.71637i) q^{88} +(-6.54765 - 11.3409i) q^{89} +(-0.169863 + 2.99519i) q^{90} +(10.2024 - 5.55302i) q^{91} +(-0.888355 + 1.53868i) q^{92} +(-1.41772 - 5.96154i) q^{93} -12.2426 q^{94} +3.95072 q^{95} +(0.400725 + 1.68506i) q^{96} +(0.883722 - 1.53065i) q^{97} +(-6.99115 - 0.351971i) q^{98} +(-10.7668 - 7.05790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{14} + 7 q^{15} + 12 q^{16} + 7 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} + 17 q^{21} - 7 q^{22} - 9 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} + 7 q^{30} - 18 q^{31} + 12 q^{32} + 3 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} + 14 q^{38} - 14 q^{39} + 6 q^{40} + q^{41} + 17 q^{42} + 7 q^{43} - 7 q^{44} - 5 q^{45} - 9 q^{46} - 14 q^{47} + 2 q^{48} - 24 q^{49} - 6 q^{50} - 3 q^{51} + 2 q^{52} + 2 q^{53} + 11 q^{54} - 14 q^{55} + 8 q^{56} - 14 q^{57} - 9 q^{58} - 58 q^{59} + 7 q^{60} + 22 q^{61} - 18 q^{62} - 13 q^{63} + 12 q^{64} + 4 q^{65} + 3 q^{66} + 44 q^{67} + 7 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - 4 q^{72} + 6 q^{73} - 12 q^{74} + 5 q^{75} + 14 q^{76} - 23 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} - 4 q^{81} + q^{82} - 26 q^{83} + 17 q^{84} - 7 q^{85} + 7 q^{86} - 12 q^{87} - 7 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} - 26 q^{93} - 14 q^{94} + 28 q^{95} + 2 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^14 + 7 * q^15 + 12 * q^16 + 7 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 + 17 * q^21 - 7 * q^22 - 9 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 + 7 * q^30 - 18 * q^31 + 12 * q^32 + 3 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 + 14 * q^38 - 14 * q^39 + 6 * q^40 + q^41 + 17 * q^42 + 7 * q^43 - 7 * q^44 - 5 * q^45 - 9 * q^46 - 14 * q^47 + 2 * q^48 - 24 * q^49 - 6 * q^50 - 3 * q^51 + 2 * q^52 + 2 * q^53 + 11 * q^54 - 14 * q^55 + 8 * q^56 - 14 * q^57 - 9 * q^58 - 58 * q^59 + 7 * q^60 + 22 * q^61 - 18 * q^62 - 13 * q^63 + 12 * q^64 + 4 * q^65 + 3 * q^66 + 44 * q^67 + 7 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - 4 * q^72 + 6 * q^73 - 12 * q^74 + 5 * q^75 + 14 * q^76 - 23 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 - 4 * q^81 + q^82 - 26 * q^83 + 17 * q^84 - 7 * q^85 + 7 * q^86 - 12 * q^87 - 7 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 - 26 * q^93 - 14 * q^94 + 28 * q^95 + 2 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more